In an experiment, the interior of a first current-carrying toroid with 1000 turns per unit length is filled with aluminum (susceptibility 2.4 × 10^ -5 ). A second, identical toroid with 500 turns per unit length is

Question

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Correct answer: B. 4:1

The magnetic field inside a toroid with a core is given by

B = \mu_0 (1 + \chi) n I

.

The magnetic field without the core is

B_0 = \mu_0 n I

.

The increase in the magnetic field due to the core is

\Delta B = B - B_0 = \mu_0 \chi n I

.

For the first toroid:

n_1 = 1000

\chi_1 = 2.4 \times 10^{-5}

\Delta B_1 = \mu_0 \chi_1 n_1 I

For the second toroid:

n_2 = 500

\chi_2 = 1.2 \times 10^{-5}

\Delta B_2 = \mu_0 \chi_2 n_2 I

The ratio of the increase in their magnetic fields is:

\dfrac{\Delta B_1}{\Delta B_2} = \dfrac{\chi_1 n_1}{\chi_2 n_2} = \dfrac{2.4 \times 10^{-5} \times 1000}{1.2 \times 10^{-5} \times 500} = 2 \times 2 = 4

The ratio is

4:1

.

Answer:

4:1

In an experiment, the interior of a first current-carrying toroid...

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