Magnetic torque on sphere on inclined plane

[eagleswings]

[SOLVED] Magnetic torque on sphere on inclined plane

Homework Statement

a nonconducting sphere has mass 80 g and radius 20 cm. a flat, compact coil of wire with 5 turns is wrapped tightly around it, with each turn concentric with the sphere. the sphere is placed on an inclined plane that slopes downward to the left, making an angle theta with the horizontal so that the coil is parallel to the inclined plane. a uniform magnetic field of .35 Tesla vertically upward exists in the region of the sphere. what current in the coil will enable the sphere to rest in equilibrium on the inclined plane? show that the result does not depend on the value of theta.

Homework Equations

F = q(v x B)(nAL), Tau = mu x B, and mu of coil = NIA

The Attempt at a Solution

mu of coil = NIA = 5 (I)(2piR) = 5(2pi)(20)(I)
so mu of coil = 100 (pi)(I)

then Tau = mg sin theta = mu x B sin theta = NIA (B) sin theta
so I = mg sin theta/(NAB sin theta)
substituting I = .08(6.673 x 10 -11)/(5 pi)(2 x 10 -2) squared (.35)
= (.53384)(x 10 -11)/(21.99 x 10 -4) = 243 x 10 -11

but the book answer is .713 Amps CCW, so i am off by a factor of a trillion or so again :-(

 

[eagleswings]

i needed the formula Torque = r cross mg, and i needed to use little g acceleration and not big G gravitational constant. that solves it.

 

[Moetasim]

The magnetic torque on a sphere on an inclined plane is a result of the interaction between the magnetic field and the current in the coil. This torque can be calculated using the equation Tau = mu x B, where mu is the magnetic moment of the coil, B is the magnetic field, and x represents the cross product. In this case, the magnetic moment of the coil can be found by multiplying the number of turns (N), the current (I), and the area of the coil (A).

To determine the current needed to achieve equilibrium, we can set the magnetic torque equal to the gravitational torque (mg sin theta) and solve for I. However, it is important to note that the angle theta does not affect the result, as shown by the fact that it cancels out in the final equation. This is because the magnetic torque is always perpendicular to the plane and therefore does not change with the angle of the incline.

In this case, the correct answer is .713 Amps CCW. It is possible that there was an error in the calculations, or that the units were not converted correctly. It is important to carefully check all calculations and units to ensure accurate results in scientific experiments.