A non conducting sphere has more 80.0 g and radius 20.0 cm. A flat, compact coil

Question

A non conducting sphere has more 80.0 g and radius 20.0 cm. A flat, compact coil of wire with six turns is wrapped tightiy around it,with each turn concentric with the sphere. The sphere is placed on an inclined plane that slopes downward to the left (see figure below),making an angle theta with horizontal do that the coil is parallel to the inclined plane. A uniform magnetic field of 0.315 T vertically unward exists in the region of the sphere. what current (magnitude and direction) in the coil will enable the sphere to rest in equilibrium on the include plane?

Explanation / Answer

The sphere is in translational equilibrium,thus

fs - mgsin(theta) = 0 .....................(1)

The sphere is in rotational equilibrium. If torques are taken about the center of the sphere, the magnetic field produces a clockwise torque of magnitude uBsin(theta), and the frictional force a counterclockwise torque of magnitude fsR, where R is the radius of the sphere.

Thus:

fsR - uBsin(theta) = 0 ...........(2)

from equation (1)

fs = mgsin(theta) put this value in equation (1)

mgsin(theta)*R = uBsin(theta)

uB = mgR ............(3)

Now, u = NIpiR^2 put this value in equation (3)

I = mg / NpiBR

I = (0.08 kg*9.8 m/s^2) / (6*3.14*0.315 T*0.20 m)

I = 0.660 Amp

The current must be counterclockwise

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.