First slide

Magnetic field due to a current carrying circular ring

Question

A length of wire caries a steady current. First it is bent to form a circular coil of one tum. Then it is bent more sharply to form a loop of two turns but of smaller radius. Now the magnetic flux density at the centre caused by same current is found to be such that

Moderate

A

magnetic flux density of double loop = 1/4 that of single turn coil
B

it is four times that of single turn coil
C

it is same and remains unaltered
D

it is one-half of the first value

Solution

B = $B_{1} = \frac{μ_{0} N i}{2 R} L = N \times 2 π R B_{2} = \frac{μ_{0} 2 N i}{2 \frac{R}{2}} L = 2 N \times 2 π \frac{R}{2} B_{2} = 4 B_{1}$

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