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Two concentric coils each of radius equal to 2 π cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m2 at the center of the coils will be 7
(μ0 = 4π x 10-7 Wb/A.m)
- a)10-5
- b)12 x 10-5
- c)7 x 10-5
- d)5 x 10-5
Correct answer is option 'D'. Can you explain this answer?
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Two concentric coils each of radius equal to 2 π cm are placed at rig...
The magnetic field due to circular coil (1) is
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Magnetic field due to coil (2) Total magnetic field
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Two concentric coils each of radius equal to 2 π cm are placed at rig...
Given:
Radius of each coil, r = 2π cm = 2π x 10^-2 m
Current in the first coil, I1 = 3 A
Current in the second coil, I2 = 4 A
Magnetic induction at the center of the coils, B = ?
The magnetic field at the center of a circular coil is given by the formula:
B = (μ0 * n * I) / (2 * r)
where,
B is the magnetic induction,
μ0 is the permeability of free space, which is equal to 4π x 10^-7 Wb/A.m,
n is the number of turns per unit length,
I is the current flowing through the coil, and
r is the radius of the coil.
Since the coils are concentric and at right angles to each other, the magnetic fields produced by each coil at the center will be perpendicular to each other. Therefore, the net magnetic field at the center will be the vector sum of the individual magnetic fields.
To find the net magnetic field, we can use the principle of superposition. The magnetic field due to the first coil is given by:
B1 = (μ0 * n1 * I1) / (2 * r)
And the magnetic field due to the second coil is given by:
B2 = (μ0 * n2 * I2) / (2 * r)
Since the coils are concentric, the number of turns per unit length for both coils will be the same. Therefore, n1 = n2 = n.
The net magnetic field at the center is given by:
B = √(B1^2 + B2^2)
Substituting the values and squaring both sides:
B^2 = (B1^2 + B2^2)
B^2 = [(μ0 * n * I1) / (2 * r)]^2 + [(μ0 * n * I2) / (2 * r)]^2
B^2 = (μ0^2 * n^2 * (I1^2 + I2^2)) / (4 * r^2)
B^2 = (4π^2 x 10^-14 * n^2 * (9 + 16)) / (4 * (2π)^2 x 10^-4)
B^2 = (4π^2 x 10^-14 * n^2 * 25) / (4 * 4π^2 x 10^-4)
B^2 = 25 x 10^-10 n^2 / 4
B^2 = 6.25 x 10^-10 n^2
Since the magnetic field at the center is given as 7 x 10^-5 Wb/m^2, we can equate this to B^2:
6.25 x 10^-10 n^2 = 7 x 10^-5
n^2 = (7 x 10^-5) / (6.25 x 10^-10)
n^2 = 1120
n = √1120 ≈ 33.47
Therefore, the number of turns per unit length, n = 33.47.
Hence, the correct answer is option D) 5 x 10^-5.
Radius of each coil, r = 2π cm = 2π x 10^-2 m
Current in the first coil, I1 = 3 A
Current in the second coil, I2 = 4 A
Magnetic induction at the center of the coils, B = ?
The magnetic field at the center of a circular coil is given by the formula:
B = (μ0 * n * I) / (2 * r)
where,
B is the magnetic induction,
μ0 is the permeability of free space, which is equal to 4π x 10^-7 Wb/A.m,
n is the number of turns per unit length,
I is the current flowing through the coil, and
r is the radius of the coil.
Since the coils are concentric and at right angles to each other, the magnetic fields produced by each coil at the center will be perpendicular to each other. Therefore, the net magnetic field at the center will be the vector sum of the individual magnetic fields.
To find the net magnetic field, we can use the principle of superposition. The magnetic field due to the first coil is given by:
B1 = (μ0 * n1 * I1) / (2 * r)
And the magnetic field due to the second coil is given by:
B2 = (μ0 * n2 * I2) / (2 * r)
Since the coils are concentric, the number of turns per unit length for both coils will be the same. Therefore, n1 = n2 = n.
The net magnetic field at the center is given by:
B = √(B1^2 + B2^2)
Substituting the values and squaring both sides:
B^2 = (B1^2 + B2^2)
B^2 = [(μ0 * n * I1) / (2 * r)]^2 + [(μ0 * n * I2) / (2 * r)]^2
B^2 = (μ0^2 * n^2 * (I1^2 + I2^2)) / (4 * r^2)
B^2 = (4π^2 x 10^-14 * n^2 * (9 + 16)) / (4 * (2π)^2 x 10^-4)
B^2 = (4π^2 x 10^-14 * n^2 * 25) / (4 * 4π^2 x 10^-4)
B^2 = 25 x 10^-10 n^2 / 4
B^2 = 6.25 x 10^-10 n^2
Since the magnetic field at the center is given as 7 x 10^-5 Wb/m^2, we can equate this to B^2:
6.25 x 10^-10 n^2 = 7 x 10^-5
n^2 = (7 x 10^-5) / (6.25 x 10^-10)
n^2 = 1120
n = √1120 ≈ 33.47
Therefore, the number of turns per unit length, n = 33.47.
Hence, the correct answer is option D) 5 x 10^-5.
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Two concentric coils each of radius equal to 2 π cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m2 at the center of the coils will be 7(μ0 = 4π x 10-7 Wb/A.m)a)10-5b)12 x 10-5c)7 x 10-5d)5 x 10-5Correct answer is option 'D'. Can you explain this answer?
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Two concentric coils each of radius equal to 2 π cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m2 at the center of the coils will be 7(μ0 = 4π x 10-7 Wb/A.m)a)10-5b)12 x 10-5c)7 x 10-5d)5 x 10-5Correct answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two concentric coils each of radius equal to 2 π cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m2 at the center of the coils will be 7(μ0 = 4π x 10-7 Wb/A.m)a)10-5b)12 x 10-5c)7 x 10-5d)5 x 10-5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two concentric coils each of radius equal to 2 π cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m2 at the center of the coils will be 7(μ0 = 4π x 10-7 Wb/A.m)a)10-5b)12 x 10-5c)7 x 10-5d)5 x 10-5Correct answer is option 'D'. Can you explain this answer?.
Two concentric coils each of radius equal to 2 π cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m2 at the center of the coils will be 7(μ0 = 4π x 10-7 Wb/A.m)a)10-5b)12 x 10-5c)7 x 10-5d)5 x 10-5Correct answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two concentric coils each of radius equal to 2 π cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m2 at the center of the coils will be 7(μ0 = 4π x 10-7 Wb/A.m)a)10-5b)12 x 10-5c)7 x 10-5d)5 x 10-5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two concentric coils each of radius equal to 2 π cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m2 at the center of the coils will be 7(μ0 = 4π x 10-7 Wb/A.m)a)10-5b)12 x 10-5c)7 x 10-5d)5 x 10-5Correct answer is option 'D'. Can you explain this answer?.
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