Question

A closely wound solenoid of length 1 m has 5 layers of 500 turns each. If the magnitude of the magnetic field inside the solenoid near its centre is 4.4 mT, find the current carried.

• A. 1.4 A
• B. 1.5 A
• C. 1.6 A
• D. 1.8 A

Hint:

Magnetic field inside solenoid: \(B = \mu_0 n I\), total turns per unit length includes all layers.

Answer 1

The Correct Option is A

Step 1: Find the turns per unit length.
Five layers of 500 turns each give $N = 2500$ turns over a length of $1\ \text{m}$, so $n = 2500\ \text{turns/m}$.
Step 2: Write the solenoid field equation, simplifying the $\pi$'s early.
\[ B = \mu_0 n I \implies I = \frac{B}{\mu_0 n} \]
Since $\mu_0 n = (4\pi\times10^{-7})(2500) = 10000\pi\times10^{-7} = \pi\times10^{-3}$, the $\pi$ stays as one clean factor.
Step 3: Substitute and divide.
\[ I = \frac{4.4\times10^{-3}}{\pi\times10^{-3}} = \frac{4.4}{\pi} \approx 1.4\ \text{A} \]
\[ \boxed{1.4\ \text{A}} \]