Question

A circular current carrying loop having 100 turns and radius $10cm$ is placed in x-y plane as shown in figure. A uniform magnetic field $\overrightarrow{B}=-(\hat{i}+\hat{k})$ tesla is present in the region. If current in the loop is $5A$, then Match the following:

Answer 1

A. $M=N/A=100\times \pi \times \pi {(0.1}^2=5\pi Am$
As current in xy plane is along anticlockwise direction, so moment will be along z-axis by right hand thumb rule
$\overrightarrow{M}=5\pi \hat{k}$
B. $\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}=5\pi \hat{k}(-\overrightarrow{\tau }+\hat{k})=-5\pi \hat{j}$
C. Net force on a closed current carrying loop in a uniform magnetic field is zero.
D. Magnetic field at centre of loop due to current in loop will be along positive z-axis from right hand thumb rule.