4. Mutual Inductance and Self-Inductance

Concept Explanation:
- Mutual Inductance: Mutual inductance occurs when a changing current in one coil induces an EMF in a nearby coil. The mutual inductance M between two coils depends on the geometry of the coils and their relative position.

Formula for Mutual Inductance:
EMF_2 = -M dI_1/dt
where:
- EMF_2 is the induced EMF in the second coil,
- M is the mutual inductance,
- dI_1/dt is the rate of change of current in the first coil.

- Self-Inductance: Self-inductance is the property of a coil (or any circuit) by which a changing current in the same coil induces an EMF in it. The self-inductance L of a coil depends on its geometry and the number of turns.

Formula for Self-Inductance:
EMF = -L dI/dt
where:
- L is the self-inductance of the coil,
- dI/dt is the rate of change of current in the coil.

Example Problem:
A coil with a self-inductance of 0.5 H has a current that changes at a rate of 2 A/s. Calculate the induced EMF.

Solution:
Using the formula for self-inductance:
EMF = -L dI/dt
EMF = -0.5 × 2 = -1 V
The induced EMF is 1 V, with the negative sign indicating the direction of the induced EMF opposes the change in current.