Force and Torque on Current Loops Practice Problems

Considering the loop shown in the figure below, determine the amount of rotation that is required for the loop to reach its equilibrium position.

Imagine that a magnetic field of 0.60 T causes a small bar magnet to undergo a torque of 0.0125 N•m when its axis is inclined to 60°. Under these conditions, what would be the magnitude of the magnetic dipole moment for this particular magnet?

Consider a current-carrying wire placed close to a current-carrying loop as shown in the figure. What is the magnitude of the torque exerted by the wire on the current-carrying loop?

Consider the two conductors given in the diagram. The length and width of the loop are 6.0 cm and 4.0 cm, respectively. This loop carries a direct current of magnitude of 5.0 Amps. The second conductor is an infinitely long wire with a direct current of 15 Amps. Compute the net force and torque exerted by the infinitely long wire over the rectangular loop.

As a materials scientist, you are studying the magnetic properties of an aluminum plate that has the following dimensions: length = 25 cm, width = 15 cm, and thickness = 12 mm. Each aluminum atom has a magnetic dipole moment of approximately -7 × 10⁻²³ A•m².

(a) Calculate the total magnetic dipole moment for the saturated aluminum plate.

(b) Determine the torque exerted on the plate when it is placed in a -75 T magnetic field acting at right angles.

What current is needed in order for full-scale deflection on a galvanometer to occur if the magnetic field strength decreases to 0.60 of its initial value, given that it originally deflects fully at 50.0 μA?

What current will give full-scale deflection if the spring in a galvanometer loses 20% of its stiffness and it originally required 30 μA?

How does the resulting torque change if the current supplied to a winch motor is reduced by 22%?

A circular coil with a radius of 12 cm is placed in a uniform magnetic field in such a way that the plane of the coil is perpendicular to the field lines. If the coil carries a current of 5.0 A and experiences a torque of 0.30 N⋅m, calculate the magnitude of the magnetic field strength.

What is the maximum torque on a 18-turn square coil (4.0 cm per side) that spins in a 0.030 T magnetic field, if a motor powered by a 8.0-V battery has a total resistance of 22 Ω?