Magnetic Effects Of Current Question 14
Question 14 - 2024 (31 Jan Shift 2)
A uniform magnetic field of $2 \times 10^{-3} \mathrm{~T}$ acts along positive Y-direction. A rectangular loop of sides $20 \mathrm{~cm}$ and $10 \mathrm{~cm}$ with current of $5 \mathrm{~A}$ is $\mathrm{Y}-\mathrm{Z}$ plane. The current is in anticlockwise sense with reference to negative $\mathrm{X}$ axis. Magnitude and direction of the torque is :
(1) $2 \times 10^{-4} \mathrm{~N}-\mathrm{m}$ along positive Z-direction
(2) $2 \times 10^{-4} \mathrm{~N}-\mathrm{m}$ along negative Z-direction
(3) $2 \times 10^{-4} \mathrm{~N}-\mathrm{m}$ along positive $\mathrm{X}$-direction
(4) $2 \times 10^{-4} \mathrm{~N}-\mathrm{m}$ along positive $\mathrm{Y}$-direction
Show Answer
Answer: (2)
Solution:
$\overrightarrow{\mathrm{M}}=\mathrm{i} \overrightarrow{\mathrm{A}}$
$=5 \times(0.2) \times(0.1)(-\hat{\mathrm{i}})$
$=0.1(-\hat{\mathrm{i}})$
$\vec{\tau}=\overrightarrow{\mathrm{M}} \times \overrightarrow{\mathrm{B}}=0.1(-\hat{\mathrm{i}}) \times\left(2 \times 10^{-3}\right)(\hat{\mathrm{j}})$
$=2 \times 10^{-4}(-\hat{\mathrm{k}}) \mathrm{N}-\mathrm{m}$
