Question

A long solenoid has \(1000\) turns per meter and carries a current of \(2\,A\). The magnetic field inside the solenoid is: \[ (\mu_0 = 4\pi \times 10^{-7}\,TmA^{-1}) \]

• A. \(8\pi \times 10^{-4}\,T\)
• B. \(4\pi \times 10^{-4}\,T\)
• C. \(2\pi \times 10^{-4}\,T\)
• D. \(16\pi \times 10^{-4}\,T\)

Hint:

For long solenoids: \[ B\propto nI \] Increasing turns or current increases magnetic field strength.

Answer 1

The Correct Option is A

Concept: Magnetic field inside a long solenoid is: \[ B=\mu_0 n I \] where:

• \(B\) = magnetic field
• \(n\) = turns per unit length
• \(I\) = current

Step 1: Write the formula. \[ B=\mu_0 nI \]

Step 2: Substitute values. \[ B= (4\pi \times 10^{-7}) \times1000 \times2 \] \[ = 8\pi \times10^{-4}\,T \]

Step 3: Final answer. \[ \boxed{ 8\pi \times10^{-4}\,T } \]