Magnetic Field Produced by Loops and Solenoids Practice Problems

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.

A coil made of tightly wound aluminum wire is intended to generate a magnetic field of strength 0.063 T at its center. The length of the coil is 45.0 cm, and its diameter is 2.0 cm. Determine the minimum number of turns per unit length needed if the aluminum wire used is rated to carry a maximum current of 20.0 A. Treat the coil like a solenoid since the length is much greater than the radius.

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 closed loop with negligible resistance and a radius of 1.5 mm is placed in the x-y plane. A current of intensity 125 A flows counterclockwise through the loop. Determine the magnetic dipole moment of the loop.

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.

A long wire is meticulously coiled to form 150 loops that are arranged in a precise manner to create a solenoid. Each loop generates a magnetic dipole moment of 5.0 × 10 ^-4 A•m². The interior volume of the solenoid is 35 × 10 ^-6 m³. Determine the magnitude of the magnetic field within the solenoid.

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.

What is the magnetic field strength at the center of a spinning disk with a flat, circular shape, uniformly charged to 2 C and having a radius of 0.1 m? The disk rotates at an angular velocity of 10 rad/s around an axis passing through its center.

Consider a charged rod with a linear charge density of λ = 2.5 μC/cm at rest as shown in the figure below. A ball is moving parallel to the rod with a velocity of v = 0.15 cm/s. Determine the electric field and magnetic field at a distance of 3.5 cm above the rod as seen by a stationary observer In the ball's frame. Hint: The stationary observer detects a current, I = λ•v.

A rectangular loop of wire with dimensions of 3.0 m by 2.0 m carries a 20.0 A current. The loop weighs 3.0 kg and is hinged at one edge on a smooth horizontal surface. If the current flows in the direction shown below, what should be the strength of a uniform horizontal magnetic field so that the loop stays at an angle of 30 degrees to the horizontal surface in equilibrium?

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.

Consider a long cylindrical electrode of radius R. The electrode has a current density given by J = J₀ (1 - r/R), where J₀ is a constant, R is the electrode radius, and r is the distance from the electrode center. What is the magnitude of the magnetic field inside the electrode at a radius r if current I is passing through it?

A 300-turn solenoid used in an electronic device has a length of 15.0 cm and a cross-sectional area of 0.200 cm². The wire used for the solenoid supports a maximum current of 60.0 A. Determine energy stored in the uniform magnetic field of the solenoid at maximum current.

What is the magnetic field inside of the solenoid at its center if a solenoid has a length of 15 cm has a total of 450 turns of wire and carries a current of 2.5 A?

An engineer needs to design a solenoid that can produce an internal magnetic field strength of about 0.35 T at the center when operating at a maximum current capacity of about 3.0 A. The device will be approximately 0.50 m long and have a diameter of 1.0 cm. What should be the number of loops in the coil?

A solenoid with a total of 800 turns and a length of 20 cm carries an electric current of 45 A while oriented horizontally. A straight conducting rod of a length of 2 cm passes through its center along a diameter measuring up to about 4 cm and carries an electric current flowing upwards at a rate of about 25 A. What would be the magnitude of the force acting upon this rod if we assume that the direction of the solenoid's magnetic field points westwards?