Question

A pivoted magnetic compass needle is free to rotate in a horizontal plane in earth's magnetic field. Another magnetic field of induction $0.54\times {10}^{-4}$ Tesla is applied at right angles to the earth's field $B_H=0.36\times {10}^{-4}$ Tesla. The angle through which the needle deflects is:

• A. 50${}^0$
• B. 60${}^0$
• C. less than 60${}^0$ but greater than 45${}^0$
• D. greater than 60${}^0$

Answer 1

The correct option is C less than 60${}^0$ but greater than 45${}^0$

Given,
induction of the magnetic field is,
$B=0.54\times {10}^{-4}$
Horizontal component of the magnetic field,
$B_H=0.36\times {10}^{-4}$
The deflections of the needle is $\theta =ta{n}^{-1}\left(\frac{0.54\times {10}^{-4}}{0.36\times {10}^{-4}}\right)$
$\theta ={56.3}^0$