Question

A long solenoid of $50\,cm$ length having $100\,turns$ carries a current of $2.5\,A$. The magnetic field at the centre of the solenoid is : $(\mu_o = 4\pi \times 10^{-7} T\,m\,A^{-1})$

• A. $6.28 \times 10^{-4}T$
• B. $3.14 \times 10^{-4}T$
• C. $6.28 \times 10^{-5}T$
• D. $3.14 \times 10^{-5}T$

Answer 1

The Correct Option is A

Magnetic field at centre of solenoid $=\mu_{0}nI$
$n=\frac{N}{L}$
$=\frac{100}{50 \times 10^{-2}}$
$=200$ tums/m
$I = 2.5 \,A$
On putting the values,
$B=4\pi\times 10^{-7}\times 200 \times 2.5$
$=6.28 \times 10^{-4}\,T$

Answer 2

The magnetic field at the center of the solenoid = 𝜇₀nl

n = N/L = 100/(50×10-2) = 200 turns/m

I = 2.5 A

On putting the values

B = 4𝜋 × 10^-7 × 200 × 2.5

= 6.28 × 10^-4 T

The correct answer is option (A)