Question

A solenoid in MRI is 3 m long, 90 cm in diameter, and 1000 turns of superconducting wire. Find the inductance and induced emf in the solenoid when the current in the wire is changing from 0 to 3 kA in 30 s.

Answer 1

Answer on Question 48583, Physics, Electromagnetism

Question:

A solenoid in MRI is $3\mathrm{m}$ long, $90~\mathrm{cm}$ in diameter, and 1000 turns of superconducting wire. Find the inductance and induced emf in the solenoid when the current in the wire is changing from 0 to $3\mathrm{kA}$ in $30~\mathrm{s}$.

Solution:

The inductance of the solenoid follows as:

$$L = \frac {\mu_ {0} N ^ {2} \pi d ^ {2}}{4 l},$$

where $\mu_0$ is the magnetic constant, $N$ is the number of turns of wire, $d$ is the wire diameter and $l$ is the solenoid length. So, we obtain:

$$L = \frac {4 \pi \cdot 1 0 ^ {- 7} N \cdot A ^ {- 2} \cdot 1 0 0 0 ^ {2} \cdot \pi \cdot (0 . 9 m) ^ {2}}{4 \cdot 3 m} = 0. 2 6 H.$$

The formula for induced emf looks like:

$$\varepsilon = - L \frac {d I}{d t} = - L \frac {\Delta I}{\Delta t} = - L \frac {I _ {2} - I _ {1}}{t} = - 0. 2 6 H \cdot \frac {3 0 0 0 A}{3 0 s} = - 2 6 V.$$

Answer:

The inductance of solenoid is $0.26H$, the induced emf is $-26V$.

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