Question

The current of 5 A flows in a square loop of sides 1 m placed in air. The magnetic field at the center of the loop is $X\sqrt{2} \times 10^{-7} \, T$. The value of X = _________.

Answer 1

The magnetic field B is given by:

$B = 4 \times \frac{\mu_0 I}{4 \pi \left(\frac{1}{2}\right)} \left( \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} \right).$

Substituting the values:

$B = 4 \times \frac{10^{-7} \times 5}{\frac{\pi}{2}} \left( \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} \right).$

Simplifying:

$B = 4 \times \frac{10^{-7} \times 5 \times 2}{\pi} \times \frac{2}{\sqrt{2}}.$

Further simplifying:

$B = 4 \times 10^{-7} \times 5 \times 2 \times \sqrt{2}.$

$B = 40 \sqrt{2} \times 10^{-7} \, \text{T}.$

Final Answer:

$B = 40 \sqrt{2} \times 10^{-7} \, \text{T}.$