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A circular coil of radius R=10 cm having 500 turns and total resistance 2ohm is placed initially perpendicular to the earth magnetic field of 3×10^-5T. The coil is rotated about its vertical diameter by an angle π in 0.5seconds.The induced current in the coil a)0.5mA b)1.0mA c)1.5mA d)3.0mA Can you explain the answer? The answer is b?
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A circular coil of radius R=10 cm having 500 turns and total resistanc...
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A circular coil of radius R=10 cm having 500 turns and total resistanc...
Explanation:
The induced emf in a coil is given by Faraday's Law as follows:
emf = -N(dΦ/dt)
where N is the number of turns in the coil and Φ is the magnetic flux through the coil.
Finding magnetic flux:
The magnetic flux through the coil can be calculated as follows:
Φ = B.A.cosθ
where B is the magnetic field strength, A is the area of the coil, and θ is the angle between the normal to the coil and the magnetic field.
Given that the coil is initially perpendicular to the magnetic field, θ = 90°. Therefore, cosθ = 0.
Φ = B.A.0 = 0
This means that there is no magnetic flux through the coil initially.
Finding the induced emf:
When the coil is rotated by an angle of π in 0.5 seconds, the magnetic flux through the coil changes. The new magnetic flux through the coil can be calculated as follows:
Φ = B.A.cosθ
where θ is the angle between the normal to the coil and the magnetic field.
When the coil is rotated by an angle of π, θ changes from 90° to 270°. Therefore, cosθ changes from 0 to -1.
Φ = B.A.(-1) = -B.A
The change in magnetic flux is given by:
ΔΦ = Φf - Φi = -B.A - 0 = -B.A
The time taken for the coil to rotate by an angle of π is 0.5 seconds. Therefore, the average rate of change of magnetic flux is:
(dΦ/dt) = ΔΦ/Δt = (-B.A)/0.5 = -2B.A
The induced emf in the coil is therefore:
emf = -N(dΦ/dt) = 500(-2B.A) = -1000B.A
The negative sign indicates that the induced current will flow in a direction to oppose the change in magnetic flux.
Finding the induced current:
The resistance of the coil is given as 2 ohms. Therefore, the induced current in the coil is:
I = emf/R = (-1000B.A)/2 = -500B.A
The negative sign indicates that the induced current will flow in a direction opposite to the direction of the initial current.
Substituting the given values, we get:
B = 3×10^-5 T
A = πR^2 = π(0.1)^2 = 0.0314 m^2
Therefore,
I = -500(3×10^-5)(0.0314) = -0.047 mA
Since the answer cannot be negative, we take the magnitude of the answer as follows:
I = 0.047 mA
Therefore, the induced current in the coil is 0.047 mA, which is closest to option (b) 1.0 mA.
The induced emf in a coil is given by Faraday's Law as follows:
emf = -N(dΦ/dt)
where N is the number of turns in the coil and Φ is the magnetic flux through the coil.
Finding magnetic flux:
The magnetic flux through the coil can be calculated as follows:
Φ = B.A.cosθ
where B is the magnetic field strength, A is the area of the coil, and θ is the angle between the normal to the coil and the magnetic field.
Given that the coil is initially perpendicular to the magnetic field, θ = 90°. Therefore, cosθ = 0.
Φ = B.A.0 = 0
This means that there is no magnetic flux through the coil initially.
Finding the induced emf:
When the coil is rotated by an angle of π in 0.5 seconds, the magnetic flux through the coil changes. The new magnetic flux through the coil can be calculated as follows:
Φ = B.A.cosθ
where θ is the angle between the normal to the coil and the magnetic field.
When the coil is rotated by an angle of π, θ changes from 90° to 270°. Therefore, cosθ changes from 0 to -1.
Φ = B.A.(-1) = -B.A
The change in magnetic flux is given by:
ΔΦ = Φf - Φi = -B.A - 0 = -B.A
The time taken for the coil to rotate by an angle of π is 0.5 seconds. Therefore, the average rate of change of magnetic flux is:
(dΦ/dt) = ΔΦ/Δt = (-B.A)/0.5 = -2B.A
The induced emf in the coil is therefore:
emf = -N(dΦ/dt) = 500(-2B.A) = -1000B.A
The negative sign indicates that the induced current will flow in a direction to oppose the change in magnetic flux.
Finding the induced current:
The resistance of the coil is given as 2 ohms. Therefore, the induced current in the coil is:
I = emf/R = (-1000B.A)/2 = -500B.A
The negative sign indicates that the induced current will flow in a direction opposite to the direction of the initial current.
Substituting the given values, we get:
B = 3×10^-5 T
A = πR^2 = π(0.1)^2 = 0.0314 m^2
Therefore,
I = -500(3×10^-5)(0.0314) = -0.047 mA
Since the answer cannot be negative, we take the magnitude of the answer as follows:
I = 0.047 mA
Therefore, the induced current in the coil is 0.047 mA, which is closest to option (b) 1.0 mA.
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A circular coil of radius R=10 cm having 500 turns and total resistance 2ohm is placed initially perpendicular to the earth magnetic field of 3×10^-5T. The coil is rotated about its vertical diameter by an angle π in 0.5seconds.The induced current in the coil a)0.5mA b)1.0mA c)1.5mA d)3.0mA Can you explain the answer? The answer is b?
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A circular coil of radius R=10 cm having 500 turns and total resistance 2ohm is placed initially perpendicular to the earth magnetic field of 3×10^-5T. The coil is rotated about its vertical diameter by an angle π in 0.5seconds.The induced current in the coil a)0.5mA b)1.0mA c)1.5mA d)3.0mA Can you explain the answer? The answer is b? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A circular coil of radius R=10 cm having 500 turns and total resistance 2ohm is placed initially perpendicular to the earth magnetic field of 3×10^-5T. The coil is rotated about its vertical diameter by an angle π in 0.5seconds.The induced current in the coil a)0.5mA b)1.0mA c)1.5mA d)3.0mA Can you explain the answer? The answer is b? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular coil of radius R=10 cm having 500 turns and total resistance 2ohm is placed initially perpendicular to the earth magnetic field of 3×10^-5T. The coil is rotated about its vertical diameter by an angle π in 0.5seconds.The induced current in the coil a)0.5mA b)1.0mA c)1.5mA d)3.0mA Can you explain the answer? The answer is b?.
A circular coil of radius R=10 cm having 500 turns and total resistance 2ohm is placed initially perpendicular to the earth magnetic field of 3×10^-5T. The coil is rotated about its vertical diameter by an angle π in 0.5seconds.The induced current in the coil a)0.5mA b)1.0mA c)1.5mA d)3.0mA Can you explain the answer? The answer is b? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A circular coil of radius R=10 cm having 500 turns and total resistance 2ohm is placed initially perpendicular to the earth magnetic field of 3×10^-5T. The coil is rotated about its vertical diameter by an angle π in 0.5seconds.The induced current in the coil a)0.5mA b)1.0mA c)1.5mA d)3.0mA Can you explain the answer? The answer is b? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular coil of radius R=10 cm having 500 turns and total resistance 2ohm is placed initially perpendicular to the earth magnetic field of 3×10^-5T. The coil is rotated about its vertical diameter by an angle π in 0.5seconds.The induced current in the coil a)0.5mA b)1.0mA c)1.5mA d)3.0mA Can you explain the answer? The answer is b?.
Solutions for A circular coil of radius R=10 cm having 500 turns and total resistance 2ohm is placed initially perpendicular to the earth magnetic field of 3×10^-5T. The coil is rotated about its vertical diameter by an angle π in 0.5seconds.The induced current in the coil a)0.5mA b)1.0mA c)1.5mA d)3.0mA Can you explain the answer? The answer is b? in English & in Hindi are available as part of our courses for NEET.
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