Worksheet: Motion Induced emf

In this worksheet, we will practice using Faraday's law and Lenz's law to calculate the emf induced in a conductor that is moving within a magnetic field.

Q1:

An automobile with a radio antenna 1.0 m long travels at 100.0 km/h in a location where the Earth’s horizontal magnetic field is 5.5×10 T. What is the maximum possible emf induced in the antenna due to this motion?

Q2:

A coil with 50 turns and area 10 cm2 is oriented with its plane perpendicular to a 0.75-T magnetic field. If the coil is flipped over (rotated through 180) in 0.20 s, what is the average emf induced in it?

Q3:

The rod shown in the diagram moves to the right on negligible-resistance rails at a speed of 𝑣=3.0/ms. If 𝐵=0.75T everywhere in the region of the rails, what is the current through the 5.0 Ω resistor?

Q4:

The conducting rod shown in the accompanying figure moves along parallel metal rails that are 25-cm apart. The system is in a uniform magnetic field of strength 0.75 T, which is directed into the page. The resistances of the rod and the rails are negligible, but the section 𝑃𝑄 has a resistance of 0.25 Ω.

What is the magnitude of the emf induced in the rod when it is moving to the right with a speed of 5.0 m/s?

What force is required to keep the rod moving with a speed of 5.0 m/s?

What is the rate at which work is done by the force required to keep the rod moving with a speed of 5.0 m/s?

What is the power dissipated in the resistor?

Q5:

A 500-turn coil has an 0.250-m2 area. The coil is spun in Earth’s magnetic field and a 12.0-kV maximum emf is induced in the coil. Find the angular speed at which the coil must be spun to induce this emf. Use a value of 5.00×10 T for the Earth’s magnetic field magnitude.

  • A 1 . 4 7 × 1 0 rad/s
  • B 2 . 4 0 × 1 0 rad/s
  • C 1 . 8 4 × 1 0 rad/s
  • D 1 . 9 2 × 1 0 rad/s
  • E 2 . 2 3 × 1 0 rad/s

Q6:

A 25 cm rod moves at 5.0 m/s in a plane perpendicular to a magnetic field of strength 0.25 T. The rod, velocity vector, and magnetic field vector are mutually perpendicular, as indicated in the accompanying figure.

Calculate the magnetic force on an electron in the rod.

  • A5.0 N
  • B0.25 N
  • C0.31 N
  • D0.0 N
  • E1.6 N

Calculate the electric field in the rod.

Calculate the potential difference between the ends of the rod.

What would be the speed of the rod if the potential difference between the ends of the rod was 1.0 V?

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