Question

Which of the following statements are true concerning electromagnetic induction? Check all that apply? 

 A. It is possible to induce a current in a closed loop of wire located in a uniform magnetic field by either increasing or decreasing the area enclosed by the loop. 

 B. It is possible to induce a current in a closed loop of wire by change the orientation of a magnetic field enclosed by the wire. 

 C. It is possible to induce a current in a closed loop of wire by changing the strength of a magnetic field enclosed by the wire. 

 D. It is possible to induce a current in a closed loop of wire without the aid of a power supply or battery. 

 E. It is possible to induce a current in a closed loop of wire located in a uniform magnetic field.

Answer 1

Concepts and reason

The concepts of magnetic flux, induced emf and Lenz’s law are required to solve the problem.

First, determine the changes that would induce an emf in the loop by using the concept of magnetic flux. Then, determine the magnetic flux through the loop by using the relation between the magnetic field, area of the loop, and magnetic flux. The magnitude of induced emf is determined by using the change in magnetic flux during a time interval.

The magnitude of the induced current is determined by using Ohm’s law. The direction of induced current is determined by using Lenz’s law. Finally, determine the changes that would result in a clockwise emf by using Lenz’s law.

Fundamentals

The magnetic flux is defined as the number of magnetic field lines passing through a surface. The expression for magnetic flux is,

${\Phi _B} = BA\cos \theta$

Here, B is the magnetic field, A is the surface area, and $\theta$ is the angle between the magnetic field and the normal to the surface area.

The expression for the magnetic flux clearly shows that the magnetic flux dis directly proportional to the strength of the magnetic field, the area of the surface, and the orientation of the field lines in the surface.

The induced emf is directly proportional to the time rate of change of magnetic flux. The expression for induced emf is,

$\varepsilon = - \frac{{\Delta {\Phi _B}}}{{\Delta t}}$

Here, $\Delta {\Phi _B}$ is the change in magnetic flux and $\Delta t$ is the time interval.

Lenz’s law states that the current induced in a circuit due to a change in the magnetic field and the direction of induced current is such as to oppose the change in the magnetic field that produces it.

According to right hand thumb rule, curl the fingers of right hand into a half circle in such a way that the thumb points in the direction of the magnetic field, then the fingers will point in the direction of current.

(A)

If a loop of wire is placed in the uniform magnetic field going from left direction to the right direction, then by moving the length of the wire downwards through the magnetic field, no current would be induced, because, the strength of the field remains constant along its course of motion. Thus, the magnetic flux does not change.

Therefore, it is not possible to induce a current in a closed of wire located in a uniform magnetic field.

(A)

If the magnitude of magnetic field increases, the number of magnetic field lines passing through the loop will increase. Increase in the number of magnetic field lines will change the magnetic flux through the loop and the change in the magnetic flux will induce an emf in the loop.

Hence, it is possible to induce a current in a closed loop of wire located in a uniform magnetic field by either increasing or decreasing the area enclosed by the loop.

(B)

Refer the equation ${\Phi _B} = BA\cos \theta$ .

The magnetic flux is directly proportional to the angle between the magnetic field and the area vector. As the orientation of the angle changes, the magnetic flux also changes.

According to the equation $\varepsilon = - \frac{{\Delta {\Phi _B}}}{{\Delta t}}$ , the change in the orientation of the magnetic field enclosed by the wire changes the magnetic flux.

Hence, it is possible to induce a current in a closed loop of wire by changing the orientation of magnetic field enclosed by the wire.

(C)

Refer the equation ${\Phi _B} = BA\cos \theta$ .

The magnetic flux is directly proportional to the magnetic field. As the magnetic field changes, the magnetic flux also changes.

According the equation $\varepsilon = - \frac{{\Delta {\Phi _B}}}{{\Delta t}}$ , the magnetic field enclosed by the wire changes the magnetic flux thus giving rise to electromotive force and hence current.

Hence, it is possible to induce a current in a closed loop of wire by changing the strength of the magnetic field.

(D)

Refer the equation ${\Phi _B} = BA\cos \theta$ .

The magnetic flux is directly proportional to the magnetic field. As the magnetic field changes, the magnetic flux also changes.

According the equation $\varepsilon = - \frac{{\Delta {\Phi _B}}}{{\Delta t}}$ , the magnetic field enclosed by the wire changes the magnetic flux.

Hence, it is possible to induce a current in a closed loop of wire without the aid of power supply or battery.

(E)

Refer the equation ${\Phi _B} = BA\cos \theta$ .

The magnetic flux is directly proportional to the magnetic field. As the magnetic field changes, the magnetic flux also changes.

Since the wire was placed inside a uniform magnetic field there won’t be any change in the magnetic flux and hence the induced emf would be zero giving zero current.

Hence, it is not possible to induce a current in a closed loop of wire placed in a uniform magnetic field.

Ans: Part A

It is possible to induce a current in a closed loop of wire located in a uniform magnetic field by either increasing or decreasing the area enclosed by the loop.

Part B

It is possible to induce a current in a closed loop of wire by changing the orientation of magnetic field enclosed by the wire.

Part C

It is possible to induce a current in a closed loop of wire by changing the strength of magnetic field enclosed by the wire.

Part D

It is possible to induce a current in a closed loop of wire without the aid of power supply or battery.

Part E

It is not possible to induce a current in a closed loop of wire located in a uniform magnetic field.