Motional EMF Practice Problems

Consider a 25-cm-long zero-resistance metal rod that moves horizontally on frictionless, zero-resistance parallel rails at a constant speed of 12 m/s within a 0.15 T uniform magnetic field, as shown below. The rails are connected by a conducting path that has a resistance of 1.5Ω. Determine the force required to maintain the rod's speed.

A 2.0 Ω iron resistor with a 5.0 x 10^-5 kg mass is connected to a 0.20 A current for 20 seconds. Given the specific heat of iron is 449 J/kg K, calculate the temperature increase of the iron resistor.

A miniature model train carrying a 1.2 m long straight metal rod is moved along a circular track within a uniform magnetic field. The field has a strength of 2.0 × 10 ^-4 T and is oriented perpendicularly to the track. If the scientists want to measure a motional emf of 2.0 V induced in the rod, how fast should the model train travel? Assume that the motion of the rod is perpendicular to the magnetic field.

An aluminium rod of length 8.0 cm is moved through a magnetic field perpendicular to the rod, resulting in a potential difference of 0.040 V across the rod. Determine the strength and direction (inward or outward of the page) of the magnetic field in this scenario.

Consider a 25-cm-long zero-resistance metal rod that moves on frictionless, zero-resistance parallel rails at a constant speed of 12 m/s within a 0.15 T uniform magnetic field, as shown below. The rails are connected by a conducting path that has a resistance of 1.5Ω. Determine the induced current in the circuit.

A 25-cm-long metal rod is moved across a straight conducting track embedded within a uniform magnetic field. The combined resistance of the rod and track amounts to 0.15 Ω. When the rod is pushed at a constant velocity of 2.0 m/s, it causes a power loss of 6.0 W in the circuit. Determine the force required to move the rod.

A geologist is making some measurements. He places a straight horizontal wire carrying a DC current of 90.0 A towards the south. He notices that at a particular point 15.0 cm east of the wire, the Earth’s magnetic field points downward, 45° below the horizon, and has a magnitude of 4.5 x 10⁻⁵ T. Determine the total magnetic field at that point.

An engineer is designing a generator with the aim of generating a peak output voltage of 32 V. The armature is designed in a rectangular shape and has a length of 7.0 cm and a width of 5.0 cm. It rotates in a field with a strength of 0.45 T and a rate of rotation of 80 rev/s. Determine the number of circular loops of wire that would be required to be wound on the armature.

A hydroelectric plant produces an output of 85 MW at 35 kV (rms). The electricity is transported through cables with a total resistance of 5 Ω to a nearby town. What is the electromotive force at the generation point and the fraction of power lost in transmission?

A rectangular rotor blade with each blade measuring 8.0 cm by 5.0 cm is used in a small wind turbine. The rotor, made up of 75 turns of 0.65-mm-diameter copper wire, operates within a 0.70-T magnetic field. Connected to the wind turbine is an electric lamp rated at 13.5 V and 30.0 W. To supply 13.5 V to the lamp, at what rate should the turbine rotate? The resistivity of copper is $1.68 \times 10^{-8} \Omega \cdot \mathrm{m}$