# A rectangle is bent on two sides at 90 degrees so that one end lies along the xy plane while the...

## Question:

A rectangle is bent on two sides at 90 degrees so that one end lies along the xy plane while the other end lies along the xz plane. The length is {eq}a = 10{/eq} cm and {eq}b = 30{/eq} cm. At {eq}t=0{/eq}, a magnetic field of strength {eq}B = 0.1{/eq} T lies in the yz plane and points at an angle 30 degrees and 10 ms later the field points in the opposite direction.

The flux EMF induced in the rectangle is _____

## Magnetic flux:

The magnetic flux that describes the volume of the magnetic field moving across the surface of a conducting coil. Mathematically it is the multiplication of the magnetic field and the area which is vertical to the magnetic field.

## Answer and Explanation:

**Given data**

- Length of the rectangle is {eq}a = 10\;{\rm{cm}} {/eq}

- Width of the rectangle is {eq}b = 30\;{\rm{cm}} {/eq}

- Strength of the magnetic field is {eq}B = 0.1\;{\rm{T}} {/eq}

- Direction of magnetic field is {eq}\theta = 30^\circ{/eq} with yz plane.

The expression for the EMF is

{eq}\varepsilon = \dfrac{\phi }{t} = \dfrac{{AB\left( {\cos \theta - \sin \theta } \right)}}{t} {/eq}

Substituting the values,

{eq}\begin{align*} \varepsilon &= \dfrac{{10 \times 30 \times {{10}^{ - 4}} \times \left( {0.1 - \left( { - 0.1} \right)} \right)\left( {\cos 30^\circ + \sin 30^\circ } \right)}}{{10 \times {{10}^{ - 3}}}}\\ \varepsilon &= 0.81\;{\rm{V}} \end{align*} {/eq}

Therefore, the emf induced in the rectangle is {eq}0.81\;{\rm{V}}.{/eq}

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from GACE Physics (530): Practice & Study Guide

Chapter 23 / Lesson 9