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?

As an engineer in a factory, you are asked to produce a solenoid that generates a 0.150 T magnetic field at its center. The diameter of the solenoid should be 2.0 cm, and its length should be 50.0 cm. The conductor wire to be wound around a cylindrical shape is rated to carry a maximum current of 60.0 A. Determine the total length of the conductor wire needed to generate this magnetic field.

In a laboratory experiment, a solenoid made of 425 turns of copper wire arranged in a cylindrical shape is used. The length and the diameter of the solenoid are 32.0 cm and 4.0 cm, respectively. A current of 5.0 A flows through the copper wire. Determine the magnetic field at the center of the solenoid.

A current of 85 A flows through a closed loop with a radius of 1.2 mm. Calculate the magnetic field strength at point P, located 7.5 cm from the center of the loop along its central axis.

Consider a magnetic device that comprises a circular current loop with an average radius of 10 m. The wire used to construct this loop has a radius width of 4.0 cm. This loop is constructed using a superconductive material and possesses a magnetic dipole moment of 5.0 × 10⁴ A•m². Determine the current density within the loop.

A thin circular loop of wire of radius 3R carries a current I in the clockwise direction. Determine the magnetic field strength at the center of the loop.

A solenoid is used in a laboratory experiment. It is 25.0 cm long with 800 loops of wire and carries a 6.0 A current. A U-shaped copper wire carrying a 3.0-A current is placed inside the solenoid. The U-shaped wire has a side of length 10.0 cm and is perpendicular to the solenoid's magnetic field as shown. Given μ₀ =4π×10⁻⁷ T⋅m/A, what is the net force on the U-shaped wire?