First slide

Toroid

Question

A toroidal solenoid has 3000 turns and a mean radius of 10 cm. It has a soft iron core of relative permeability 2000. What is the magnitude of the magnetic field in the core when a current of 1 amp is passed through the solenoid ?

Moderate

A

0.12 T
B

0.24 T
C

1.2 T
D

12 T

Solution

The magnetic field in the core is Biven by B = $μ$ ni where n = number of turns per unit length of the solenoid.
$\begin{array}{ll} ∴ B = μ_{0} μ_{r} ni (∵ μ_{r} = μ / μ_{0}) \\ or B = 2000 \times (4 π \times 10^{- 7}) \times (\frac{3000}{2 π \times 0 \cdot 1}) \times 1 = 12 T \end{array}$

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