Two circular coils made of same material having radii 20cm & 30cm have turns 1 00 & 50 respectively. If they are connected
a) in series b) in parallel
c) separately across a source of emf find the ratio of
magnetic inductions at the centres of circles in each case

Explanation

To solve the problem of finding the ratio of magnetic inductions at the centers of two circular coils when connected in series, parallel, and separately, we will follow these steps:

### Given Data:
- Coil 1: Radius \( r_1 = 20 \, \text{cm} = 0.2 \, \text{m} \), Turns \( n_1 = 100 \)
- Coil 2: Radius \( r_2 = 30 \, \text{cm} = 0.3 \, \text{m} \), Turns \( n_2 = 50 \)

### Magnetic Induction Formula:
The magnetic induction \( B \) at the center of a circular coil is given by:
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