Exercises
Electromagnetic induction
Problems to solve on your own. The final solution appears with the button below each problem; each exercise also has its own page, to share with the link.
1. Average emf in a coil
A coil of turns, each of area , has its axis parallel to a uniform magnetic field that changes from to in . Compute the magnitude of the average emf induced in the coil.
Solution available to those who have unlocked the subject.
2. Induced charge when a loop is pulled out
A circular loop of radius and resistance is perpendicular to a uniform magnetic field of and is pulled completely out of the field region. Neglecting self-induction, compute the charge that passes through the loop.
Solution available to those who have unlocked the subject.
3. Rod at constant velocity
A conducting rod long slides at constant velocity on two rails closed by a resistor of , in a uniform magnetic field of perpendicular to the plane of the rails. Neglecting the other resistances and self-induction, compute the induced emf and the current.
Solution available to those who have unlocked the subject.
4. Force needed to pull a rod
A rod long is pulled without friction at constant velocity on two rails closed by a resistor of , in a uniform field of perpendicular to the plane of the rails. Neglecting the other resistances and self-induction, compute the force to be applied to the rod and the power it develops.
Solution available to those who have unlocked the subject.
5. Terminal velocity on vertical rails
A rod of mass and length falls without friction along two vertical rails connected at the top by a resistor of , in a uniform horizontal field of perpendicular to the plane of the rails. Neglecting the other resistances and self-induction, compute the terminal velocity.
Solution available to those who have unlocked the subject.
6. Coil rotating in a uniform field
A coil of turns of area rotates at revolutions per minute about an axis perpendicular to a uniform magnetic field of . Compute the maximum value and the frequency of the induced emf.
Solution available to those who have unlocked the subject.
7. Inductance of a solenoid
An air-core solenoid long has turns of radius . Neglecting edge effects, compute its inductance.
Solution available to those who have unlocked the subject.
8. Self-induced emf with a sinusoidal current
An inductor of inductance carries the current , with and frequency . Compute the maximum value of the self-induced emf.
Solution available to those who have unlocked the subject.
9. Closing an RL circuit
An ideal source of , a resistor of and an ideal inductor of are connected in series, and the switch is closed at time . Compute the time constant and the current at time .
Solution available to those who have unlocked the subject.
10. Halving of the current in an RL circuit
An inductor of , carrying a current, is closed at time on a resistor of , after the source has been cut out. Compute after how much time the current has halved.
Solution available to those who have unlocked the subject.
11. Magnetic energy in an air gap
In the air gap of an electromagnet, a region of air of volume , the magnetic field is uniform and equals . Compute the magnetic energy density and the energy contained in the air gap.
Solution available to those who have unlocked the subject.
12. Mutual inductance of a coil inside a solenoid
A long solenoid with turns per meter contains at its center a coaxial coil of turns of radius . Compute the mutual inductance and the magnitude of the emf induced in the coil when the current in the solenoid changes by per second.
Solution available to those who have unlocked the subject.
13. Electric field induced by a solenoid
In a long solenoid of radius the magnetic field is uniform and increases by per second. Compute the magnitude of the induced electric field at and at from the axis.
Solution available to those who have unlocked the subject.