Question

A square coil, enclosing an area with sides 2.0 cm long, is wrappedwith 2 500 turns of wire.
A uniform magnetic field perpendicular to its plane is turned onand increases to 0.25 T
during an interval of 1.0 s. What average voltage is induced in thecoil?

Answer 1

Concepts and reason

The required concepts to solve the problem are induce emf and magnetic flux.

First, find the change in magnetic flux using the magnetic field and area. Then find the voltage induced in the coil using the change in magnetic flux.

Fundamentals

The magnetic flux is defined as the surface integral of the normal component of the magnetic field passing through the that surface.

The magnetic flux is given by

Here, is the magnetic field andis the surface area.

The change in magnetic flux creates an emf called induced emf. The induced emf is given by the equation,

$N-=3 $

Here, is the number of turns, is the change in magnetic flux.

The negative sign indicates that the current produced is opposite in direction to the change in direction of the magnetic field.

The area of the square coil is,

$A=1 $

Here, is the length of the side of the square coil.

Substituteforto find the area.

The change in magnetic flux is,

Substitutefor.

Substitutefor, forandfor.

The equation for induced emf is,

Substitutefor .

$ε=-ΝΔΦ $

Substituteforand forto find.

The negative sign indicates that the current produced is opposite in direction to the change in direction of the magnetic field.

The magnitude of the induced emf is,

Ans:

The average voltage induced in the coil is.