19. [1/2 Points]
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SERPSE10 28.5.P.031.CTX.
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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
$\theta$, 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 76.0 g, and a radius 21.0 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 0.345 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.)
15.1
X
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 $\theta$ of the plane to make the required current lower. How do you respond?
The current is proportional to $\cos(\theta)$. Therefore, you cannot reduce the current by lowering the plane.
The current is independent of the angle $\theta$. Therefore, you cannot reduce the current by lowering the plane.
The current is proportional to $\sin(\theta)$. Therefore, you can reduce the current by lowering the plane.
