Magnetic Effects of Electric Current
Magnetic Field Due to a Current-Carrying Circular Loop
कक्षा 10 विज्ञान | Class 10 Science | CBSE + Foundation + Competitive
Magnetic Field Due to a Current-Carrying Circular Loop
1. Introduction | परिचय
English:
When electric current passes through a circular conducting loop, a magnetic field is produced around the loop. The magnetic field at the centre of the loop is directed perpendicular to the plane of the loop.
हिन्दी:
जब किसी वृत्ताकार चालक कुंडली में विद्युत धारा प्रवाहित की जाती है, तो उसके चारों ओर चुंबकीय क्षेत्र उत्पन्न होता है। कुंडली के केन्द्र पर चुंबकीय क्षेत्र की दिशा कुंडली के तल के लंबवत होती है।
When electric current passes through a circular conducting loop, a magnetic field is produced around the loop. The magnetic field at the centre of the loop is directed perpendicular to the plane of the loop.
हिन्दी:
जब किसी वृत्ताकार चालक कुंडली में विद्युत धारा प्रवाहित की जाती है, तो उसके चारों ओर चुंबकीय क्षेत्र उत्पन्न होता है। कुंडली के केन्द्र पर चुंबकीय क्षेत्र की दिशा कुंडली के तल के लंबवत होती है।
2. Magnetic Field Pattern of a Circular Loop | चुंबकीय क्षेत्र की आकृति
A current-carrying circular loop produces magnetic field lines that pass through the centre of the loop. Near the centre, the field lines become nearly parallel to one another.
वृत्ताकार धारा-वाहक कुंडली के कारण उत्पन्न चुंबकीय क्षेत्र रेखाएँ कुंडली के केन्द्र से होकर गुजरती हैं। केन्द्र के पास ये रेखाएँ लगभग समानांतर दिखाई देती हैं।
वृत्ताकार धारा-वाहक कुंडली के कारण उत्पन्न चुंबकीय क्षेत्र रेखाएँ कुंडली के केन्द्र से होकर गुजरती हैं। केन्द्र के पास ये रेखाएँ लगभग समानांतर दिखाई देती हैं।
Orange arrows = Current Direction | नीले तीर = Magnetic Field
3. Direction of Magnetic Field | चुंबकीय क्षेत्र की दिशा
The direction of magnetic field around a circular loop can be determined using the Right-Hand Thumb Rule.
Hold the circular loop with the fingers of your right hand in the direction of current. Your thumb then points towards the magnetic field direction through the centre of the loop.
यदि उँगलियाँ धारा की दिशा में मोड़ी जाएँ, तो दायाँ अंगूठा कुंडली के केन्द्र पर चुंबकीय क्षेत्र की दिशा बताता है।
यदि उँगलियाँ धारा की दिशा में मोड़ी जाएँ, तो दायाँ अंगूठा कुंडली के केन्द्र पर चुंबकीय क्षेत्र की दिशा बताता है।
| Current Direction | धारा की दिशा | Magnetic Field at Centre | केन्द्र पर क्षेत्र |
|---|---|
| Anticlockwise | वामावर्त | Out of the plane / बाहर की ओर |
| Clockwise | दक्षिणावर्त | Into the plane / अन्दर की ओर |
Memory Trick:
Anticlockwise Current → Magnetic field comes OUT of the page.
Clockwise Current → Magnetic field goes IN to the page.
याद रखें:
वामावर्त धारा → क्षेत्र बाहर की ओर।
दक्षिणावर्त धारा → क्षेत्र अन्दर की ओर।
Anticlockwise Current → Magnetic field comes OUT of the page.
Clockwise Current → Magnetic field goes IN to the page.
याद रखें:
वामावर्त धारा → क्षेत्र बाहर की ओर।
दक्षिणावर्त धारा → क्षेत्र अन्दर की ओर।
4. Magnetic Field at the Centre of a Circular Loop
For a circular loop of radius R carrying current I, the magnetic field at its centre is:
B = μ₀I / 2R
Where:
B = Magnetic field at centre
I = Current through the loop
R = Radius of circular loop
μ₀ = Permeability of free space
Where:
B = Magnetic field at centre
I = Current through the loop
R = Radius of circular loop
μ₀ = Permeability of free space
In SI units:
μ₀ = 4π × 10⁻⁷ T m A⁻¹
Therefore,
B = (4π × 10⁻⁷ × I) / (2R)
5. Effect of Current on Magnetic Field | धारा का प्रभाव
From the formula:
If current is doubled while radius remains constant, magnetic field becomes twice.
यदि धारा दोगुनी कर दी जाए और त्रिज्या समान रहे, तो केन्द्र पर चुंबकीय क्षेत्र भी दोगुना हो जाएगा।
B ∝ I
Thus, if current increases, the magnetic field at the centre also increases.
Example:If current is doubled while radius remains constant, magnetic field becomes twice.
यदि धारा दोगुनी कर दी जाए और त्रिज्या समान रहे, तो केन्द्र पर चुंबकीय क्षेत्र भी दोगुना हो जाएगा।
6. Effect of Radius | त्रिज्या का प्रभाव
From:
समान धारा के लिए छोटी त्रिज्या वाली कुंडली के केन्द्र पर चुंबकीय क्षेत्र अधिक होता है।
B ∝ 1/R
Therefore, for the same current, a smaller circular loop produces a stronger magnetic field at its centre than a larger loop.
समान धारा के लिए छोटी त्रिज्या वाली कुंडली के केन्द्र पर चुंबकीय क्षेत्र अधिक होता है।
7. Effect of Number of Turns | फेरों की संख्या का प्रभाव
If a circular coil has N turns, the magnetic field at its centre is:
यदि कुंडली में फेरों की संख्या बढ़ाई जाती है, तो केन्द्र पर चुंबकीय क्षेत्र भी बढ़ जाता है।
B = μ₀NI / 2R
Therefore:
B ∝ N
The magnetic field increases when the number of turns increases.
यदि कुंडली में फेरों की संख्या बढ़ाई जाती है, तो केन्द्र पर चुंबकीय क्षेत्र भी बढ़ जाता है।
Important Formula:
For a single circular turn: B = μ₀I / 2R
For N circular turns: B = μ₀NI / 2R
For a single circular turn: B = μ₀I / 2R
For N circular turns: B = μ₀NI / 2R
8. Factors Affecting Magnetic Field
| Factor | Effect on B |
|---|---|
| Current I increases | Magnetic field increases |
| Number of turns N increases | Magnetic field increases |
| Radius R increases | Magnetic field decreases |
| Current direction reverses | Magnetic field direction reverses |
9. Magnetic Field Lines Around a Circular Loop
The magnetic field lines of a circular loop are similar to the magnetic field pattern of a bar magnet.
One face of the loop behaves like a magnetic north pole and the other face behaves like a magnetic south pole.
वृत्ताकार कुंडली का चुंबकीय क्षेत्र पैटर्न बार मैग्नेट के क्षेत्र जैसा होता है। कुंडली का एक फलक उत्तर ध्रुव तथा दूसरा फलक दक्षिण ध्रुव जैसा व्यवहार कर सकता है।
वृत्ताकार कुंडली का चुंबकीय क्षेत्र पैटर्न बार मैग्नेट के क्षेत्र जैसा होता है। कुंडली का एक फलक उत्तर ध्रुव तथा दूसरा फलक दक्षिण ध्रुव जैसा व्यवहार कर सकता है।
Important:
The magnetic field is stronger where magnetic field lines are closer together.
जहाँ चुंबकीय क्षेत्र रेखाएँ अधिक पास-पास होती हैं, वहाँ चुंबकीय क्षेत्र अधिक प्रबल होता है।
The magnetic field is stronger where magnetic field lines are closer together.
जहाँ चुंबकीय क्षेत्र रेखाएँ अधिक पास-पास होती हैं, वहाँ चुंबकीय क्षेत्र अधिक प्रबल होता है।
10. Direction Using Clock Face Rule
When a circular coil is viewed from one side:
Anticlockwise current → that face behaves as North Pole.
Clockwise current → that face behaves as South Pole.
हिन्दी:
वामावर्त धारा दिखाई दे तो वह फलक उत्तर ध्रुव जैसा व्यवहार करता है।
दक्षिणावर्त धारा दिखाई दे तो वह फलक दक्षिण ध्रुव जैसा व्यवहार करता है।
Anticlockwise current → that face behaves as North Pole.
Clockwise current → that face behaves as South Pole.
हिन्दी:
वामावर्त धारा दिखाई दे तो वह फलक उत्तर ध्रुव जैसा व्यवहार करता है।
दक्षिणावर्त धारा दिखाई दे तो वह फलक दक्षिण ध्रुव जैसा व्यवहार करता है।
11. Comparison with a Straight Conductor
| Straight Conductor | Circular Loop |
|---|---|
| Field lines are concentric circles around conductor. | Field lines pass through and around the loop. |
| Field depends on current and distance. | At centre, B = μ₀NI/2R. |
| Direction by Right-Hand Thumb Rule. | Direction also determined using right-hand rule. |
12. Numerical Example | संख्यात्मक उदाहरण
Question:
A circular coil of radius 0.1 m carries a current of 2 A. Find the magnetic field at its centre.
Solution:
I = 2 A
R = 0.1 m
B = (4π × 10⁻⁷ × 2)/(2 × 0.1)
B = 4π × 10⁻⁶ T
Approximately: B ≈ 1.26 × 10⁻⁵ T
A circular coil of radius 0.1 m carries a current of 2 A. Find the magnetic field at its centre.
Solution:
B = μ₀I / 2R
μ₀ = 4π × 10⁻⁷ T m A⁻¹I = 2 A
R = 0.1 m
B = (4π × 10⁻⁷ × 2)/(2 × 0.1)
B = 4π × 10⁻⁶ T
Approximately: B ≈ 1.26 × 10⁻⁵ T
13. Important Conceptual Points
1. A current-carrying circular loop produces a magnetic field.
2. At the centre of the loop, the magnetic field is perpendicular to the plane of the loop.
3. Magnetic field increases with current.
4. Magnetic field increases with number of turns.
5. Magnetic field decreases with radius.
6. Reversing current reverses magnetic field direction.
7. A circular loop can behave like a bar magnet.
2. At the centre of the loop, the magnetic field is perpendicular to the plane of the loop.
3. Magnetic field increases with current.
4. Magnetic field increases with number of turns.
5. Magnetic field decreases with radius.
6. Reversing current reverses magnetic field direction.
7. A circular loop can behave like a bar magnet.
14. 30 MCQs | बहुविकल्पीय प्रश्न
1. A current-carrying circular loop produces:
धारा-वाहक वृत्ताकार कुंडली उत्पन्न करती है:
धारा-वाहक वृत्ताकार कुंडली उत्पन्न करती है:
A. Only electric field
B. Only heat
C. Magnetic field
D. Gravitational field
Answer: C
A current-carrying conductor produces a magnetic field.
A current-carrying conductor produces a magnetic field.
2. The magnetic field at the centre of a circular loop is directed:
A. Along the radius
B. Perpendicular to the plane of loop
C. Along the circumference
D. Randomly
Answer: B
3. For a single circular loop, magnetic field at centre is:
A. μ₀I/2R
B. μ₀IR/2
C. 2μ₀R/I
D. μ₀/IR
Answer: A
4. If current is doubled, magnetic field at centre becomes:
A. Half
B. Same
C. Double
D. Four times
Answer: C
5. Magnetic field at centre is inversely proportional to:
A. Current
B. Number of turns
C. Radius
D. μ₀
Answer: C
6. For N turns, magnetic field at centre is:
A. μ₀I/2NR
B. μ₀NI/2R
C. 2μ₀R/NI
D. μ₀R/NI
Answer: B
7. If number of turns is increased, magnetic field:
A. Decreases
B. Increases
C. Becomes zero
D. Remains unchanged
Answer: B
8. Anticlockwise current in a loop makes the viewed face behave like:
A. South pole
B. Neutral face
C. North pole
D. Electric pole
Answer: C
9. Clockwise current in a loop makes the viewed face behave like:
A. North pole
B. South pole
C. Both poles
D. No pole
Answer: B
10. SI unit of magnetic field is:
A. Weber
B. Tesla
C. Ampere
D. Volt
Answer: B
11. μ₀ represents:
A. Electric charge
B. Resistance
C. Permeability of free space
D. Current
Answer: C
12. The magnetic field is stronger where field lines are:
A. Far apart
B. Closer together
C. Absent
D. Random
Answer: B
13. If radius becomes twice, keeping current same, B becomes:
A. Twice
B. Four times
C. Half
D. Same
Answer: C
14. Magnetic field is directly proportional to:
A. Radius
B. Current
C. 1/current
D. 1/turns
Answer: B
15. The direction of magnetic field can be determined by:
A. Right-hand rule
B. Ohm's law
C. Joule's law
D. Archimedes principle
Answer: A
16. If current direction is reversed, magnetic field direction:
A. Remains same
B. Reverses
C. Becomes zero
D. Doubles
Answer: B
17. For a coil with 10 turns, compared with one turn under same I and R, B is:
A. 10 times
B. 5 times
C. 1/10
D. Same
Answer: A
18. The field at the centre of circular loop is:
A. Zero always
B. Perpendicular to loop plane
C. Along circumference
D. Along radius
Answer: B
19. A circular coil behaves magnetically similar to:
A. Battery
B. Resistor
C. Bar magnet
D. Capacitor
Answer: C
20. Which change increases B most directly?
A. Decreasing current
B. Increasing radius
C. Increasing number of turns
D. Reversing current only
Answer: C
21. The magnetic field formula for N turns is:
A. B = μ₀NI/2R
B. B = 2R/μ₀NI
C. B = μ₀R/2NI
D. B = NI/μ₀R
Answer: A
22. If both I and N are doubled, B becomes:
A. Half
B. Double
C. Four times
D. Same
Answer: C
23. If I is doubled and R is doubled, B becomes:
A. Same
B. Double
C. Half
D. Four times
Answer: A
24. Which quantity has unit tesla?
A. Current
B. Magnetic field
C. Charge
D. Resistance
Answer: B
25. The field at the centre increases when radius:
A. Increases
B. Decreases
C. Becomes infinite
D. Has no effect
Answer: B
26. The magnetic field of a loop depends on:
A. Current
B. Radius
C. Number of turns
D. All of these
Answer: D
27. In the formula B = μ₀NI/2R, B is measured in:
A. Tesla
B. Volt
C. Ohm
D. Joule
Answer: A
28. A smaller loop with the same current produces at centre:
A. Smaller B
B. Greater B
C. Zero B
D. Same B always
Answer: B
29. Which rule helps determine the direction of magnetic field?
A. Right-hand thumb rule
B. Fleming's left-hand rule only
C. Ohm's law
D. Snell's law
Answer: A
30. For a circular coil, increasing turns generally makes the magnetic field:
A. Weaker
B. Stronger
C. Zero
D. Unchanged
Answer: B
15. 30 Subjective Questions with Answers
2 Marks
1. What happens when current flows through a circular loop?
1. What happens when current flows through a circular loop?
A magnetic field is produced around the circular loop.
At the centre, the field is perpendicular to the plane of the loop.
2 Marks
2. State the direction of magnetic field at the centre of a loop carrying anticlockwise current.
2. State the direction of magnetic field at the centre of a loop carrying anticlockwise current.
The magnetic field is directed out of the plane of the loop towards the observer.
2 Marks
3. What happens to magnetic field when current is reversed?
3. What happens to magnetic field when current is reversed?
The direction of magnetic field reverses.
2 Marks
4. Write the SI unit of magnetic field.
4. Write the SI unit of magnetic field.
The SI unit of magnetic field is tesla (T).
2 Marks
5. Write the formula for magnetic field at the centre of a circular loop.
5. Write the formula for magnetic field at the centre of a circular loop.
For one turn:
B = μ₀I/2R
For N turns:
B = μ₀NI/2R.
3 Marks
6. State three factors affecting magnetic field at the centre of a circular coil.
6. State three factors affecting magnetic field at the centre of a circular coil.
The magnetic field depends on:
1. Current I
2. Number of turns N
3. Radius R
B increases with I and N but decreases with R.
3 Marks
7. Explain the effect of increasing current on magnetic field.
7. Explain the effect of increasing current on magnetic field.
For a circular coil:
B = μ₀NI/2R
For constant N and R:
B ∝ I
Therefore, increasing current increases the magnetic field proportionally.
3 Marks
8. Explain the effect of radius on magnetic field.
8. Explain the effect of radius on magnetic field.
B = μ₀NI/2R
Therefore:
B ∝ 1/R
Hence, increasing radius decreases magnetic field at the centre.
3 Marks
9. Why does increasing the number of turns increase magnetic field?
9. Why does increasing the number of turns increase magnetic field?
Each turn produces its own magnetic field. The fields of the turns add together at the centre. Therefore, increasing the number of turns increases the resultant magnetic field.
3 Marks
10. How does a circular loop behave like a bar magnet?
10. How does a circular loop behave like a bar magnet?
A current-carrying circular loop produces a magnetic field pattern similar to that of a bar magnet. One face behaves as a north pole and the other as a south pole.
4 Marks
11. Derive the relation for magnetic field at the centre of a circular loop.
11. Derive the relation for magnetic field at the centre of a circular loop.
For a circular loop of radius R carrying current I, the magnetic field at its centre is:
B = μ₀I/2R
If there are N turns, each turn contributes equally, so:
B = N(μ₀I/2R)
Therefore:
B = μ₀NI/2R
4 Marks
12. Explain the right-hand rule for a circular loop.
12. Explain the right-hand rule for a circular loop.
Curl the fingers of your right hand in the direction of current through the loop. The extended thumb gives the direction of magnetic field through the centre of the loop.
4 Marks
13. A coil has 20 turns. What happens to its field if turns are increased to 40?
13. A coil has 20 turns. What happens to its field if turns are increased to 40?
Since B ∝ N:
B₂/B₁ = 40/20 = 2
Therefore, magnetic field becomes twice the original value, if current and radius remain unchanged.
4 Marks
14. A circular coil has current 4 A. If current becomes 8 A, compare magnetic fields.
14. A circular coil has current 4 A. If current becomes 8 A, compare magnetic fields.
B ∝ I
Therefore:
B₂/B₁ = 8/4 = 2
The new magnetic field is twice the original magnetic field.
4 Marks
15. What happens if radius of a coil is reduced to half?
15. What happens if radius of a coil is reduced to half?
Since B ∝ 1/R:
If R₂ = R₁/2,
B₂/B₁ = R₁/R₂ = 2.
Therefore, magnetic field becomes twice.
5 Marks
16. Explain the factors responsible for strength of magnetic field at the centre of a circular coil.
16. Explain the factors responsible for strength of magnetic field at the centre of a circular coil.
According to:
B = μ₀NI/2R
1. B increases with current I.
2. B increases with number of turns N.
3. B decreases with radius R.
4. μ₀ is constant for free space.
5. Reversing current changes direction, not the magnitude if I remains the same.
5 Marks
17. Explain how direction of current determines polarity of a circular coil.
17. Explain how direction of current determines polarity of a circular coil.
Viewed from one face:
Anticlockwise current → North pole.
Clockwise current → South pole. This follows from the right-hand rule.
Anticlockwise current → North pole.
Clockwise current → South pole. This follows from the right-hand rule.
5 Marks
18. Explain the magnetic field pattern of a current-carrying circular loop.
18. Explain the magnetic field pattern of a current-carrying circular loop.
The field lines emerge from one face and enter the other face outside the loop, forming a pattern similar to a bar magnet. Near the centre, the field lines are nearly parallel and perpendicular to the plane of the loop.
5 Marks
19. Why is a coil with many turns used to obtain a strong magnetic field?
19. Why is a coil with many turns used to obtain a strong magnetic field?
The magnetic field due to each turn adds to the fields produced by other turns. Since:
B ∝ N
increasing the number of turns increases the resultant magnetic field.
5 Marks
20. Calculate B for N = 100, I = 2 A and R = 0.1 m.
20. Calculate B for N = 100, I = 2 A and R = 0.1 m.
B = μ₀NI/2R
= (4π×10⁻⁷ ×100×2)/(2×0.1)
= 4π×10⁻⁴ T
≈ 1.26×10⁻³ T.
6 Marks
21. Explain the working principle of a current-carrying circular loop as an electromagnet.
21. Explain the working principle of a current-carrying circular loop as an electromagnet.
When current flows through the loop, it produces a magnetic field. Increasing current or number of turns strengthens the field. The direction of the field depends on current direction. Thus, a current-carrying coil can act as a controllable magnet.
6 Marks
22. Compare a single loop and a coil of N turns.
22. Compare a single loop and a coil of N turns.
| Single Loop | N-turn Coil |
|---|---|
| B = μ₀I/2R | B = μ₀NI/2R |
| One turn contributes. | N turns contribute. |
| Comparatively weaker. | Comparatively stronger. |
6 Marks
23. Explain how magnetic field can be increased without increasing current.
23. Explain how magnetic field can be increased without increasing current.
From B = μ₀NI/2R, magnetic field can be increased by:
1. Increasing number of turns N.
2. Decreasing radius R, if the arrangement permits.
3. Using an appropriate magnetic core in practical coil systems where applicable.
1. Increasing number of turns N.
2. Decreasing radius R, if the arrangement permits.
3. Using an appropriate magnetic core in practical coil systems where applicable.
6 Marks
24. A coil has radius 20 cm and current 5 A. Explain how its magnetic field changes if radius is reduced to 10 cm.
24. A coil has radius 20 cm and current 5 A. Explain how its magnetic field changes if radius is reduced to 10 cm.
Since B ∝ 1/R:
R₁ = 20 cm
R₂ = 10 cm
B₂/B₁ = R₁/R₂ = 20/10 = 2.
Therefore, the magnetic field becomes twice, provided current and number of turns remain unchanged.
6 Marks
25. Why does reversing current reverse magnetic field?
25. Why does reversing current reverse magnetic field?
The direction of magnetic field is linked to the direction of current according to the right-hand rule. When current direction is reversed, the curling direction of the magnetic field also reverses.
6 Marks
26. Explain the importance of circular coils in electromagnets.
26. Explain the importance of circular coils in electromagnets.
Circular turns concentrate and add their magnetic fields. By using many turns and suitable current, a strong magnetic field can be produced. Such coils are therefore important components of electromagnets and other electrical devices.
6 Marks
27. What happens to B if current, number of turns and radius are all doubled?
27. What happens to B if current, number of turns and radius are all doubled?
B = μ₀NI/2R
New values:
N' = 2N
I' = 2I
R' = 2R
Therefore:
B'/B = (2N × 2I)/(2R) ÷ (NI/R) = 2
Hence, magnetic field becomes twice.
6 Marks
28. A circular coil produces magnetic field B. What will happen if current is halved and radius is also halved?
28. A circular coil produces magnetic field B. What will happen if current is halved and radius is also halved?
B ∝ I/R.
Both I and R are halved:
B'/B = (I/2)/(R/2) × R/I = 1.
Therefore, magnetic field remains unchanged.
6 Marks
29. Explain why the magnetic field near the centre of a circular loop is nearly uniform.
29. Explain why the magnetic field near the centre of a circular loop is nearly uniform.
Near the centre, contributions from different portions of the circular loop combine symmetrically. The field direction changes very little over a small central region, so field lines are approximately parallel and the field can be considered nearly uniform there.
6 Marks
30. Write a complete summary of the magnetic field due to a circular loop.
30. Write a complete summary of the magnetic field due to a circular loop.
A current-carrying circular loop produces a magnetic field. At its centre the field is perpendicular to the plane of the loop. Its magnitude for N turns is:
B = μ₀NI/2R
The field increases with current and number of turns and decreases with radius. Its direction is determined by the right-hand rule. A circular current-carrying coil behaves magnetically like a bar magnet.
16. Assertion–Reason Questions
Assertion (A):
The magnetic field at the centre of a circular coil increases when current is increased.
Reason (R): The magnetic field at the centre is directly proportional to current.
Reason (R): The magnetic field at the centre is directly proportional to current.
Answer: Both A and R are true, and R correctly explains A.
Assertion (A):
Increasing the radius of a circular coil increases the magnetic field at its centre.
Reason (R): B is inversely proportional to radius.
Reason (R): B is inversely proportional to radius.
Answer: A is false, but R is true.
Assertion (A):
Increasing the number of turns increases the magnetic field.
Reason (R): Magnetic fields produced by the turns add at the centre.
Reason (R): Magnetic fields produced by the turns add at the centre.
Answer: Both A and R are true, and R correctly explains A.
Assertion (A):
Reversing current reverses the direction of magnetic field.
Reason (R): Magnetic field direction depends on current direction.
Reason (R): Magnetic field direction depends on current direction.
Answer: Both A and R are true, and R correctly explains A.
17. HOTS Questions | उच्च स्तरीय प्रश्न
HOTS 1:
Two coils have the same current and same number of turns. Coil A has radius 10 cm and Coil B has radius 20 cm. Which coil has stronger field at the centre?
Two coils have the same current and same number of turns. Coil A has radius 10 cm and Coil B has radius 20 cm. Which coil has stronger field at the centre?
Since B ∝ 1/R, the coil with smaller radius produces the stronger field. Therefore, Coil A has stronger magnetic field.
HOTS 2:
A coil has 50 turns. If the number of turns is increased to 150 without changing current and radius, how does B change?
A coil has 50 turns. If the number of turns is increased to 150 without changing current and radius, how does B change?
B ∝ N.
Therefore:
B₂/B₁ = 150/50 = 3.
The magnetic field becomes three times.
HOTS 3:
If both current and radius of a circular coil are reduced to half, what happens to the magnetic field?
If both current and radius of a circular coil are reduced to half, what happens to the magnetic field?
B ∝ I/R.
Both I and R are halved, so their ratio remains unchanged.
Therefore, magnetic field remains unchanged.
18. One-Minute Revision | एक मिनट में Revision
🧲 Current + Circular Loop → Magnetic Field
Formula: B = μ₀NI/2R
Remember: I ↑ → B ↑
N ↑ → B ↑
R ↑ → B ↓
Direction: Anticlockwise → North face → Field outward
Clockwise → South face → Field inward
Memory Trick: “More Current + More Turns = More Magnetic Field”
“More Radius = Less Field”
Formula: B = μ₀NI/2R
Remember: I ↑ → B ↑
N ↑ → B ↑
R ↑ → B ↓
Direction: Anticlockwise → North face → Field outward
Clockwise → South face → Field inward
Memory Trick: “More Current + More Turns = More Magnetic Field”
“More Radius = Less Field”
19. Quick Concept Map
Electric Current
↓
Circular Loop
↓
Magnetic Field
↓
Direction by Right-Hand Rule
↓
B = μ₀NI/2R
20. Exam Golden Points
✔ Current-carrying circular loop produces magnetic field.
✔ Magnetic field at centre is perpendicular to the plane of loop.
✔ B = μ₀NI/2R
✔ B increases with current.
✔ B increases with number of turns.
✔ B decreases with radius.
✔ Reversal of current reverses magnetic field direction.
✔ Anticlockwise current → North face.
✔ Clockwise current → South face.
✔ A circular current-carrying coil behaves like a bar magnet.
✔ Magnetic field at centre is perpendicular to the plane of loop.
✔ B = μ₀NI/2R
✔ B increases with current.
✔ B increases with number of turns.
✔ B decreases with radius.
✔ Reversal of current reverses magnetic field direction.
✔ Anticlockwise current → North face.
✔ Clockwise current → South face.
✔ A circular current-carrying coil behaves like a bar magnet.
21. Final Summary | अंतिम सारांश
English:
A current-carrying circular loop produces a magnetic field. The magnetic field at the centre of the loop is perpendicular to its plane. For a coil having N turns, current I and radius R, the field at the centre is given by:
हिन्दी:
धारा-वाहक वृत्ताकार कुंडली चुंबकीय क्षेत्र उत्पन्न करती है। कुंडली के केन्द्र पर चुंबकीय क्षेत्र उसके तल के लंबवत होता है। N फेरों वाली कुंडली के लिए:
A current-carrying circular loop produces a magnetic field. The magnetic field at the centre of the loop is perpendicular to its plane. For a coil having N turns, current I and radius R, the field at the centre is given by:
B = μ₀NI/2R
The magnetic field increases with current and number of turns and decreases with radius. Its direction is determined using the right-hand rule. The magnetic field pattern of a circular coil resembles that of a bar magnet.
हिन्दी:
धारा-वाहक वृत्ताकार कुंडली चुंबकीय क्षेत्र उत्पन्न करती है। कुंडली के केन्द्र पर चुंबकीय क्षेत्र उसके तल के लंबवत होता है। N फेरों वाली कुंडली के लिए:
B = μ₀NI/2R
चुंबकीय क्षेत्र धारा और फेरों की संख्या बढ़ने पर बढ़ता है तथा त्रिज्या बढ़ने पर घटता है। चुंबकीय क्षेत्र की दिशा दाएँ हाथ के नियम से निर्धारित की जाती है। वृत्ताकार कुंडली का चुंबकीय क्षेत्र बार मैग्नेट के समान होता है।
Magnetic Effects of Electric Current
Magnetic Field Due to a Current-Carrying Circular Loop
Class 10 Science | CBSE | Foundation | Competitive Preparation
Magnetic Field Due to a Current-Carrying Circular Loop
Class 10 Science | CBSE | Foundation | Competitive Preparation
