Find the self-inductance of a toroidal solenoid of radius 20 cm, area of cross section `100 cm^(2)` and having 500 turns. Assume that the field variations across the cross section of the toroid are negligible. Further, if a secondary coil of 300 turns is wound on this toroid and the current in the primary coil is increased from 2 A to 5 A in 0.05 s. Find the emf induced in the secondary coil.

Explanation

To solve the problem step by step, we will first find the self-inductance of the toroidal solenoid and then calculate the induced EMF in the secondary coil.

### Step 1: Convert the given dimensions to SI units
- Radius \( r = 20 \, \text{cm} = 0.20 \, \text{m} \)
- Area \( A = 100 \, \text{cm}^2 = 100 \times 10^{-4} \, \text{m}^2 = 0.01 \, \text{m}^2 \)

### Step 2: Calculate the length of the toroid
The length \( L \) of the toroid can be calculated using the formula for the circumference of a circle:
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