Question

A long solenoid is formed by winding 70 turns cm-1. If 2.0 A current flows, then the magnetic field produced inside the solenoid is _________ (µ0 = 4π × 10-7 TmA-1)

• A. 1232 × 10–4T
• B. 176 × 10–4T
• C. 352 × 10–4T
• D. 88 × 10–4T

Answer 1

Answer: (B)

176 × 10–4T

Answer 2

To find the magnetic field inside a solenoid, we can use the formula for the magnetic field inside an ideal solenoid:
$B = \mu_0 n I$
Given:
Number of turns per cm = 70turns/cm,
Current I = 2A.
Convert the number of turns per cm to turns per meter (since the SI unit of length is meter):
$n = 70 \, \text{turns/cm} \times 100 \, \text{cm/m} = 7000 \, \text{turns/m}$

$B = \mu_0 n I$
$B = (4\pi \times 10^{-7} \, \text{T m/A}) \times (7000 \, \text{turns/m}) \times (2 \, \text{A})$
$B = 4\pi \times 10^{-7} \times 7000 \times 2$
$B = 4\pi \times 14000 \times 10^{-7}$
$B = 56000\pi \times 10^{-7}$
$B = 5.6\pi \times 10^{-3} \, \text{T}$
$B = 5.6 \times 3.14 \times 10^{-3} \, \text{T}$
$B = 17.584 \times 10^{-3} \, \text{T}$
$B = 0.0176 \, \text{T}$
$B = 176 \times 10^{-4} \text{T}$

So, the correct option is (B): $176 \times 10^{-4} \text{T}$