### Magnetic Effects Of Current Question 14

#### Question 14 - 2024 (31 Jan Shift 2)

A uniform magnetic field of $2 \times 10^{-3} T$ acts along positive Y-direction. A rectangular loop of sides $20 cm$ and $10 cm$ with current of $5 A$ is $Y-Z$ plane. The current is in anticlockwise sense with reference to negative $X$ axis. Magnitude and direction of the torque is :

(1) $2 \times 10^{-4} N-m$ along positive Z-direction

(2) $2 \times 10^{-4} N-m$ along negative Z-direction

(3) $2 \times 10^{-4} N-m$ along positive $X$-direction

(4) $2 \times 10^{-4} N-m$ along positive $Y$-direction

## Show Answer

#### Answer: (2)

#### Solution:

$\overrightarrow{M}=i \overrightarrow{A}$

$=5 \times(0.2) \times(0.1)(-\hat{i})$

$=0.1(-\hat{i})$

$\vec{\tau}=\overrightarrow{M} \times \overrightarrow{B}=0.1(-\hat{i}) \times\left(2 \times 10^{-3}\right)(\hat{j})$

$=2 \times 10^{-4}(-\hat{k}) N-m$