Magnetic Force on Current-Carrying Wire Practice Problems

A current-carrying straight conductor is placed inside a solenoid perpendicularly to its axis. As shown in the figure, the current of magnitude 3.0 A is flowing along the positive y-direction. The current is perpendicular to the 1.50 T uniform magnetic field, directed along the positive x-direction. Calculate i) the magnitude and ii) the direction of the magnetic force exerted on a 2 cm-long segment of the conductor.

A student connected a voltage source and a 30.0 Ω resistor in series to two metallic supports of negligible resistance. Then the student laid a copper rod of mass m = 400.0 g and length l = 30.0 cm horizontally on the two supports.  Finally, a uniform magnetic field of magnitude 0.80 T directed horizontally and perpendicular to the rod was introduced. i) Calculate the maximum voltage (V_max) the student can apply without causing the rod to levitate. ii) If the student reduced the resistor value by 10 times while setting the voltage to V_max, what would be the rod's initial acceleration?

A segment of a long current-carrying conductor is placed within a uniform 0.340 T magnetic field, pointing directly out of the plane of the page. The conductor makes two right-angle turns and is positioned as shown in the figure. A current of I = 5.00 A flows within the conductor. What are i) the magnitude and ii) the direction of the magnetic force acting on the conductor due to the magnetic field?

A 1.0 m long conductor rod transporting a current of 1.5 A is brought between Helmholtz coils. The magnetic field between the two coils is uniform, directed along the positive y-axis, and has a magnitude of 80.0 μT. Calculate the force exerted by the Helmholtz coil on the wire if the current flows along i) the positive x-direction, ii) the positive z-direction, and iii) the negative y-direction. iv) Would the magnetic force deform the rod?

A long current-carrying conductor oriented parallel to the y-axis lies in a perpendicular magnetic field given by B = B₀y²/L k̂ for the interval 0 < y < L. B is zero outside these limits. A current, I, flows through the conductor in the positive y-direction. Derive an equation for torque on the conductor about the point y = 0.

A long straight copper rod with a linear mass density of m/L is suspended using massless strings. A current is sent through the rod. A vertically upward magnetic force displaces the rod by θ degrees, measured from the vertical. What is the strength of the magnetic field? Use symbols as necessary.

The two wires shown below transmit DC current at a potential of 800 kV. What resistance in the circuit will create a 6.00 N repulsive force on a 20.0 m parallel segment of the wires separated by 0.45 m?

Three identical wires with a linear mass density of 25 g/m are assembled to form an isosceles triangle with a base angle of 45 degrees.  The currents are equal, and the directions are as shown. The two base wires have a separation of 1.5 cm and are fixed to a bench. Calculate the value of the current that causes the top wire to get suspended, forming a base angle of 45 degrees.

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?

A straight wire carries a current of 5.0 A and is placed in a uniform magnetic field of strength 1.0 T at an angle of 90° and 45° to the field, respectively. What is the magnetic force per meter on the wire in each case?

A student is experimenting in her physics lab. She places a wire carrying a current of 4.75 A between the poles of a magnet. When positioned just right, the wire experiences a maximum force of 2.10 N. The pole of the magnet face has a diameter of 45.0 cm. She is curious to know the approximate strength of the magnetic field between the poles.

During a short circuit, estimate the force that Earth's magnetic field can exert on a horizontal power line. Assume that the current flowing through the power line is approximately 40000 A and that the power line is 10 meters long. The magnetic field of Earth is vertical, with a strength of roughly 50 µT. The angle between the current (flowing horizontally) and the magnetic field of Earth (vertical) is 90 degrees. Given these conditions, calculate the magnitude of the magnetic force acting on the power line.