A circular wire loop of mass M and radius R carries a current I . It hangs from a hinge that allows it to swing in the direction perpendicular to the plane of the loop. A uniform magnetic field B exists everywhere in space pointing upwards. What angle theta does the plane of the loop make with the vertical when it is in static equilibrium?

Question

A circular wire loop of mass M and radius R carries a current I . It hangs from a hinge that allows it to swing in the direction perpendicular to the plane of the loop. A uniform magnetic field B exists everywhere in space pointing upwards. What angle theta does the plane of the loop make with the vertical when it is in static equilibrium?

a)theta=pi/2
b)theta=arcsin(BIRpi/(Mg))
c)theta=arcsin(Mg/BIRpi)
d)theta=arctan(BIRpi/Mg)
e)theta=arcsin(Mg/BIRpi)

Answer 1

a)theta=pi/2

Answer 2

To find the angle θ at which the plane of the loop makes with the vertical when it is in static equilibrium, we need to consider the forces acting on the loop.

The force acting on the loop is the weight Mg acting downward and the magnetic force Fm acting upward due to the interaction with the magnetic field B. The magnetic force can be calculated using the formula Fm = BIL, where L is the circumference of the loop.

In static equilibrium, the net force acting on the loop must be zero. Therefore, the weight force Mg should balance the magnetic force Fm.

Setting up the equation:
Mg = Fm
Mg = BIL

Now, we need to express the current in terms of the given parameters. The current I can be calculated using the formula I = Q/t, where Q is the charge and t is the time. Since the current is given, we don't have to calculate it.

Next, we need to express the circumference L in terms of the given parameters. The circumference of a circle is given by L = 2πR.

Substituting the values:
Mg = BIR

Now, we can solve for θ by rearranging the equation. Divide both sides of the equation by BIRπ:

θ = Mg/BIRπ

So, the correct answer is c) θ = arcsin(Mg/BIRπ).