$[1/2$ Points$]$

SERPSE$1028\mathrm{.}5.$P$\mathrm{.}031.$CTX$.$

You are in charge of planning a physics magic show for an open house on your campus. You come up with the following plan for one trick. You will place a sphere on a rough inclined plane of angle $,$ as shown in the figure, and it will not roll down the incline.

Here is the secret that only you know: The sphere is nonconducting, has a mass of $76\mathrm{.}0$ g $,$ and a radius $21\mathrm{.}0$ cm $.$ A flat, compact coil of wire with five turns is wrapped tightly around it$,$ with each turn concentric with the sphere. The sphere is placed on the incline so that the coil is parallel to the plane. You establish a uniform magnetic field of $0\mathrm{.}345$ T vertically upward in the region of the sphere.

$($a$)$ What current in the coil $($in A $)$ do you need to make this trick work? $($Enter the magnitude.$)$

Write equations representing the fact that the sphere is in both translational and rotational equilibrium. Combine the equations and solve for the current. A

$($b$)$ You explain the trick to a friend in confidence and he suggests lowering the angle $$ of the plane to make the required current lower. How do you respond?

The current is proportional to $cos().$ Therefore, you cannot reduce the current by lowering the plane.

The current is independent of the angle $.$ Therefore, you cannot reduce the current by lowering the plane.

The current is proportional to $sin().$ Therefore, you can reduce the current by lowering the plane.