# A coil is wrapped with 200 turns of wire on a square frame with sides 18 cm. A magnetic field is...

## Question:

A coil is wrapped with 200 turns of wire on a square frame with sides 18 cm. A magnetic field is applied perpendicular to the plane of the coil. If the field changes uniformly from 0.5 T to 0 T in 8.0 s, find the average value of the induced emf.

## Magnetic Field:

The force line whose direction is towards the South Pole initiated from the North Pole of the magnet is responsible for the magnet's pulling force property. The space around the magnet within which these force lines exist is known as the magnetic field.

## Answer and Explanation: 1

**Given Data**

- The number of turns is: {eq}{n_t} = 200 {/eq}.

- The side of the square is: {eq}a = 18\;{\rm{cm}} = 0.18\;{\rm{m}} {/eq}.

- The initial magnetic field is: {eq}{B_i} = 0.5\;{\rm{T}} {/eq}.

- The final magnetic field is: {eq}{B_f} = 0\;{\rm{T}} {/eq}.

- The time duration is: {eq}t = 8.0\;{\rm{s}} {/eq}.

The equation to calculate the average value of the induced emf is given by,

{eq}V = - {n_t} \times {a^2} \times \dfrac{{\left( {{B_f} - {B_i}} \right)}}{t} {/eq}

Substitute all the values in the above equation.

{eq}\begin{align*} V &= - 200 \times {0.18^2} \times \dfrac{{\left( {0 - 0.5} \right)}}{8}\\ & = 0.40\;{\rm{V}} \end{align*} {/eq}

Thus, the average value of the induced emf is {eq}0.40\;{\rm{V}} {/eq}.

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Chapter 18 / Lesson 7Magnetism and electricity are closely related. When current flows in a wire, a magnetic field is generated. In this lesson, we will explore how magnetic fields can exert forces on parallel current-carrying wires.