Question

A conductor in the shape of a square of edge length 0.4m carries a current of 10amperes. Calculate the magnitude and dirn. of magnetic field at the center of the square

Answer 1

Final Answer: B = $\frac{\mu_o50\sqrt{2}}{\pi}$

Steps:

1) Now,we have a square conductor that consists of 4 identical finite lenght line conductors which is at 0.2m from centre of square.C

Current ,I = 10 A

Direction of Magnetic Field produced by all segments is same.

2) So, Magnetic Field due to finite line conductor .

$B=\frac{\mu_o I}{4 \pi*a}(\sin(\alpha) +\cos(\beta) )$

Here, $\alpha =45\degree , \beta =45\degree$

where $\alpha ,\beta$ are angles subtended at the centre of square from above and below ends of conductor .

3) $B_{net}= 4*B \\ \\ => 4*\frac{\mu_o I}{4\pi a}(\sin(\alpha)+\cos(\beta) ) \\ \\ => 4*\frac{\mu_o *10}{4\pi *0.2}(\sin(45\degree)+\cos(45\degree) ) \\ \\ => \frac{50 \sqrt{2}\mu_o}{\pi} T$

Direction :

=>If curent is in clockwise direction ,then Magnetic Field will be below the plane of conductor .

=>If curent is in anti- clockwise direction ,then Magnetic Field will be above the plane of conductor .

Answer 2

Answer:

Hope it helps

Explanation: