Explain the phenomenon of self induction and mutual induction. Define coefficient of self induction and mutual induction. Write the SI unit and dimensions of coefficient of self induction.
A potentiometer wire has a length of `4m` and a resistance of `5 Omega`. What resistance should be connected in series with a potentiomete-wire and a cell of e.m.f. `2V` having internal resistance `1Omega` to get a potential gradient of `10^(-3)V//cm` ?

Explanation

To solve the problem step by step, we will first explain the concepts of self-induction and mutual induction, then define their coefficients, and finally solve the problem regarding the potentiometer wire.

### Step 1: Explain Self-Induction and Mutual Induction

**Self-Induction:**
Self-induction is the phenomenon where a change in current in a coil induces an electromotive force (EMF) in the same coil. This occurs due to the change in magnetic flux linked with the coil. The relationship can be expressed as:
\[ \Phi \propto I \]
Where \( \Phi \) is the magnetic flux and \( I \) is the current. The proportionality constant \( L \) is called the coefficient of self-inductance:
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