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The magnetic field at the centre of a current carrying circular coil of radius 10 cm is 5 root 5 times the magnetic field at a point on its axis . The distance of the point from the centre of the coil in cm is? 1. 5 2.10 3.20 4.25?
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The magnetic field at the centre of a current carrying circular coil o...
Solution:
Given:
Radius of circular coil, r = 10 cm
Magnetic field at the centre of the coil, Bc = 5√5 Bx
We need to find the distance of the point from the centre of the coil, where the magnetic field is Bx.
Let us assume that the point is at a distance of x cm from the centre of the coil.
Magnetic field at the centre of the coil:
The magnetic field at the centre of a current carrying circular loop of radius r is given by:
Bc = µ0 I / (2r)
Where,
µ0 is the permeability of free space
I is the current flowing in the loop
r is the radius of the loop
Substituting the given values, we get:
5√5 Bx = µ0 I / (2r)
∴ Bx = (µ0 I) / (10√5)
Magnetic field on the axis of the coil:
The magnetic field on the axis of a current carrying circular loop at a distance x from the centre of the loop is given by:
Bx = (µ0 I / 2) * (R2 / (R2 + x2)3/2)
Where,
R is the radius of the loop
Substituting the given values, we get:
5√5 Bx = (µ0 I / 2) * (100 / (100 + x2)3/2)
∴ Bx = (µ0 I) / (10√5 * (100 + x2)3/2)
Equating Bx from both the equations:
(µ0 I) / (10√5) = (µ0 I) / (10√5 * (100 + x2)3/2)
∴ (100 + x2)3/2 = 1
∴ 100 + x2 = 1
∴ x = √99 = 3√11 cm
Therefore, the distance of the point from the centre of the coil is 3√11 cm, which is approximately equal to 5.3 cm.
Hence, the correct option is 4. 25.
Given:
Radius of circular coil, r = 10 cm
Magnetic field at the centre of the coil, Bc = 5√5 Bx
We need to find the distance of the point from the centre of the coil, where the magnetic field is Bx.
Let us assume that the point is at a distance of x cm from the centre of the coil.
Magnetic field at the centre of the coil:
The magnetic field at the centre of a current carrying circular loop of radius r is given by:
Bc = µ0 I / (2r)
Where,
µ0 is the permeability of free space
I is the current flowing in the loop
r is the radius of the loop
Substituting the given values, we get:
5√5 Bx = µ0 I / (2r)
∴ Bx = (µ0 I) / (10√5)
Magnetic field on the axis of the coil:
The magnetic field on the axis of a current carrying circular loop at a distance x from the centre of the loop is given by:
Bx = (µ0 I / 2) * (R2 / (R2 + x2)3/2)
Where,
R is the radius of the loop
Substituting the given values, we get:
5√5 Bx = (µ0 I / 2) * (100 / (100 + x2)3/2)
∴ Bx = (µ0 I) / (10√5 * (100 + x2)3/2)
Equating Bx from both the equations:
(µ0 I) / (10√5) = (µ0 I) / (10√5 * (100 + x2)3/2)
∴ (100 + x2)3/2 = 1
∴ 100 + x2 = 1
∴ x = √99 = 3√11 cm
Therefore, the distance of the point from the centre of the coil is 3√11 cm, which is approximately equal to 5.3 cm.
Hence, the correct option is 4. 25.
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The magnetic field at the centre of a current carrying circular coil o...
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The magnetic field at the centre of a current carrying circular coil of radius 10 cm is 5 root 5 times the magnetic field at a point on its axis . The distance of the point from the centre of the coil in cm is? 1. 5 2.10 3.20 4.25? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The magnetic field at the centre of a current carrying circular coil of radius 10 cm is 5 root 5 times the magnetic field at a point on its axis . The distance of the point from the centre of the coil in cm is? 1. 5 2.10 3.20 4.25? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnetic field at the centre of a current carrying circular coil of radius 10 cm is 5 root 5 times the magnetic field at a point on its axis . The distance of the point from the centre of the coil in cm is? 1. 5 2.10 3.20 4.25?.
The magnetic field at the centre of a current carrying circular coil of radius 10 cm is 5 root 5 times the magnetic field at a point on its axis . The distance of the point from the centre of the coil in cm is? 1. 5 2.10 3.20 4.25? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The magnetic field at the centre of a current carrying circular coil of radius 10 cm is 5 root 5 times the magnetic field at a point on its axis . The distance of the point from the centre of the coil in cm is? 1. 5 2.10 3.20 4.25? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnetic field at the centre of a current carrying circular coil of radius 10 cm is 5 root 5 times the magnetic field at a point on its axis . The distance of the point from the centre of the coil in cm is? 1. 5 2.10 3.20 4.25?.
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