Scenario$-1$: A circular loop of diameter $30cm$ carries a current of $2A.$ A flat coil of radius $12cm,$ having $500$turns

and a current of $13A,$ is concentric with the loop. The plane of the loop is perpendicular to the plane of the coil.

Assume the loop's magnetic field is uniform across the coil.

Scenario$-2$

Scenario$-2$: A positron $(e^{+})$is moving in a crossed vec$(E)$ and vec$(B)$ field enclosure. Take $|vec(v)|=600m{s}^{-1},$ and $|vec(B)|=3T.$

The diagram does not show the vec$(E)-$field direction.

NOTE: Questions $($a$),($b$)$ follow Scenario #$1,$ and $($c$),($d$)$ follow Scenario #$2.$

$($a$)$ What is the magnitude of the vec$(B)-$field produced by the loop at its center? Label each term in the formula you

use here.

$($b$)$ Find $($i$)$ the torque $($magnitude and direction$)$ on the coil due to the vec$(B)-$field produced by the loop, and $($ii$)$ how

it is related to vec$(m).$

$($c$)$ In what direction must the vec$(E)-$field be applied to cancel the vec$(B)-$field deflection altogether? No math. Draw a

diagram and explain using vector notation.

$($d$)$ You apply an vec$(E)-$field in the $-$hat$(j)$ direction of intensity $2kV{m}^{-1}.$ What are the magnitude and direction of the

positron's acceleration at this instant?