First slide

Toroid

Question

Two toroids 1 and 2 have total no. of turns 200 and 100 respectively with average radii 40 cm and 20 cm respectively. If they carry same current i, the ratio of the magnetic fields along the two loops is,

Moderate

A

1 : 2
B

1 : 1
C

4 : 1
D

2 : 1

Solution

Magnetic field inside a toroid in
$B = \frac{μ_{0} N \cdot I}{2 πR}$
$Here, \frac{B_{1}}{B_{2}} = \frac{N_{1} R_{2}}{N_{2} R_{1}} = \frac{200}{100} \frac{20}{40} = 1$
$So, \frac{B_{1}}{B_{2}} = 1$

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