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Chapter 16: Problem 25

If a coil of metal wire is kept stationary in a non-uniform magnetic field, (A) An EMF and current are both induced in the coil (B) A current but no EMF is induced in the coil (C) An EMF but no current is induced in the coil (D) Neither EMF nor current is induced in the coil

Short Answer

Expert verified
The correct answer is (A) An EMF and current are both induced in the coil, as both are induced due to the non-uniform magnetic field and the coil being made of conductive metal wire.

Step by step solution

01

Understanding Faraday's Law of Electromagnetic Induction

Faraday's law of electromagnetic induction states that an electromotive force (EMF) is induced in a closed loop of wire whenever there is a change in the magnetic field passing through the loop. Mathematically, the induced EMF (\(蔚\)) is given by the rate of change of the magnetic flux (\(桅\)) through the loop: \(蔚 = - \frac{d桅}{dt}\) Here, the negative sign implies that the EMF is induced in such a direction that it will oppose the change in magnetic flux, according to Lenz's law.
02

Examining the conditions for EMF and current induction

An EMF can be induced in a coil if there is a change in the magnetic field passing through the loop. This can happen if either the magnetic field is changing or if the coil is moving within the magnetic field. Since it is given that the coil is stationary within the non-uniform magnetic field, we have the first condition met (the magnetic field is non-uniform and changing over time). When an EMF is induced in a coil, it creates an electric field within the coil. This electric field will cause a current to flow in a closed loop (conducting wire). If the coil's wire is non-conductive, there will be no current flow despite the presence of an EMF induced in the coil. However, the question does not mention any such non-conductivity, and since it is assumed to be a metal wire, it can be considered conductive. Thus, a current will flow in the coil due to the induced EMF.
03

Evaluate the given options

Based on the understanding from the previous steps, let's now evaluate the given options: (A) An EMF and current are both induced in the coil: This is true, as both EMF and current will be induced due to the non-uniform magnetic field and the coil being made of conductive metal wire. (B) A current but no EMF is induced in the coil: This option is not correct. As per Faraday's law, a current can only be induced when there is an EMF. (C) An EMF but no current is induced in the coil: This option would have been true if the coil's wire was non-conductive (e.g., non-metallic). Since the coil is made of metal wire, it is conductive, and this option is not correct. (D) Neither EMF nor current is induced in the coil: This option is not correct since both EMF and current will be induced due to the non-uniform magnetic field and the coil is made of conductive metal wire.
04

Choose the correct answer

Based on the analysis and understanding of Faraday's law and the conditions for EMF and current induction, the correct answer is: (A) An EMF and current are both induced in the coil

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Most popular questions from this chapter

Net force on a current carrying loop kept in uniform magnetic field is zero and the torque on the loop \(\vec{\tau}=\vec{M} \times \vec{B}\), where \(M\) and \(B\) are magnetic dipole moment and magnetic field intensity, respectively. If it is free to rotate, then it will rotates about an axis passing through its centre of mass and parallel to \(\vec{\tau}\). Potential energy of the loop is given by \(U=-\vec{M} \cdot \vec{B}\). Assume a current carrying ring with its centre at the origin and having moment of inertia \(2 \times 10^{-2} \mathrm{~kg}-\mathrm{m}^{2}\) about an axis passing through one of its diameter and magnetic moment \(\vec{M}=(3 \hat{i}-4 \hat{j}) \mathrm{Am}^{2}\). At time \(t=0\), a magnetic field \(\vec{B}=(4 \hat{i}-3 \hat{j}) T\) is switched on. Then Angular acceleration of the ring at time \(t=0\) (in \(\mathrm{rad} / \mathrm{s}^{2}\) ) is (A) 5000 (B) 1250 (C) 2500 (D) Zero

Two coils of self-inductance \(4 \mathrm{H}\) and \(16 \mathrm{H}\) are wound on the same iron core. The coefficient of mutual inductance for them will be (A) \(8 \mathrm{H}\) (B) \(10 \mathrm{H}\) (C) \(20 \mathrm{H}\) (D) \(64 \mathrm{H}\)

The magnetic flux linked with a coil is \(\phi=8 t^{2}+3 t\) \(+5 \mathrm{~Wb}\). The induced EMF in the fourth second will be (A) \(145 \mathrm{~V}\) (B) \(139 \mathrm{~V}\) (C) \(67 \mathrm{~V}\) (D) \(16 \mathrm{~V}\)

A bar magnet, of magnetic moment \(M\), is placed in a magnetic field of induction \(B\). The torque exerted on it is (A) \(\vec{M} \cdot \vec{B}\) (B) \(\vec{B} \times \vec{M}\) (C) \(\vec{M} \times \vec{B}\) (D) \(-\vec{B} \cdot \vec{M}\)

Net force on a current carrying loop kept in uniform magnetic field is zero and the torque on the loop \(\vec{\tau}=\vec{M} \times \vec{B}\), where \(M\) and \(B\) are magnetic dipole moment and magnetic field intensity, respectively. If it is free to rotate, then it will rotates about an axis passing through its centre of mass and parallel to \(\vec{\tau}\). Potential energy of the loop is given by \(U=-\vec{M} \cdot \vec{B}\). Assume a current carrying ring with its centre at the origin and having moment of inertia \(2 \times 10^{-2} \mathrm{~kg}-\mathrm{m}^{2}\) about an axis passing through one of its diameter and magnetic moment \(\vec{M}=(3 \hat{i}-4 \hat{j}) \mathrm{Am}^{2}\). At time \(t=0\), a magnetic field \(\vec{B}=(4 \hat{i}-3 \hat{j}) T\) is switched on. Then Torque acting on the loop is (A) Zero (B) \(25 \hat{k} \mathrm{Nm}\) (C) \(16 \hat{k} \mathrm{Nm}\) (D) \(10 \hat{k} \mathrm{Nm}\)
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