Name: Conversion of a Galvanometer Into a Voltmeter
Uploaded: 2019-07-19
Duration: 7 min 18 s
Description: This video helps us understand the working of a galvanometer. It also teaches us how to convert it into a voltmeter of the desired range both theoretically a...

Question

Derive the torque on a rectangular current-carrying loop placed in a uniform magnetic field. Draw suitable figures. Write one application of this principle.

Accepted Answer

Let us consider a rectangular loop $A B C D$ is placed in a uniform magnetic field $B$ as shown in the figure. There is a steady current in the loop. Let the width and length of the loop be $b$ and $l$ respectively.

The force on arm $B C$ and $A D$ be $F_{A B}$ and $F_{A D}$ respectively. These forces are equal and opposite and act along the axis of the coil. Therefore, these forces will cancel each other out.

Similarly,

The forces $F_{A B}$ and $F_{C D}$ are also equal and opposite. Since these forces are not colinear, so they act as a couple.

Therefore, the magnitude of torque can be given as,

$τ = F_{A B} \frac{b}{2} \sin θ + F_{C D} \frac{b}{2} \sin θ$

$∵ |F_{A B}| = |F_{C D}| = B I l$

Therefore, we can say that,

$τ = B I (l b) \sin θ$

Area $A = l \times b$

Therefore,

$τ = B I \times A \times \sin θ$

We know that, $m = I A$

Therefore, $τ = m B \sin θ$

So, the vector form $\vec{τ} = \vec{m} \times \vec{B}$

A moving coil galvanometer is the application of this principle.

Derive the torque on a rectangular current-carrying loop placed in a uniform magnetic field. Draw suitable figures. Write one application of this principle.

Important Questions on Moving Charges and Magnetism

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