# Magnetic torque on sphere on inclined plane

• eagleswings
In summary, a non-conducting sphere with a mass of 80 g and radius of 20 cm is wrapped with a flat coil of wire with 5 turns. It is placed on an inclined plane with an angle theta and a uniform magnetic field of 0.35 Tesla exists in the region. The formula for torque is used to determine the current needed for the sphere to rest in equilibrium, which is found to be 0.713 Amps CCW. This result is independent of the value of theta.
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 :-(

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.

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.

## 1. What is magnetic torque on a sphere on an inclined plane?

Magnetic torque on a sphere on an inclined plane refers to the rotational force exerted on a spherical object placed on a tilted surface due to the interaction between its magnetic field and an external magnetic field.

## 2. How is the magnetic torque calculated?

The magnetic torque on a sphere on an inclined plane can be calculated using the equation T = mBsinθ, where T is the torque, m is the magnetic moment of the sphere, B is the external magnetic field, and θ is the angle between the magnetic field and the surface of the inclined plane.

## 3. What factors affect the magnetic torque on a sphere on an inclined plane?

The magnetic torque on a sphere on an inclined plane is affected by the strength and orientation of the external magnetic field, as well as the magnetic moment and orientation of the sphere.

## 4. How does the angle of the inclined plane affect the magnetic torque?

The angle of the inclined plane affects the magnetic torque by changing the angle between the magnetic field and the surface of the plane, which in turn affects the sinθ component in the torque equation.

## 5. Can the magnetic torque on a sphere on an inclined plane be zero?

Yes, the magnetic torque on a sphere on an inclined plane can be zero if the sphere's magnetic moment is aligned with the direction of the external magnetic field, resulting in a sinθ value of zero in the torque equation.

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