Question

The current in flowing along the path ABCD of a cube (shown in the left figure) produces a magnetic field at the centre of cube of magnitude B. Dashed line depicts the non-conducting part of the cube.

Consider a cubical shape shown to the right which is identical in size and shape to the left. If the same current now flows in along the path $DAEFGCD,$ then the magnitude of magnetic field at the ecnntre will be

• A. zero
• B. $\sqrt{2B}$
• C. $\sqrt{3B}$
• D. $B$

Answer 1

Answer: (C)

Given magnetic field due to a square loop $DABCA$ at centre of cube is $B.$

Now, loop $DAEFGCD$ can be viewed as super position of three square loops as shown below.

So, net field at centre = resultant of fields of these three loops

$\therefore B_{net}=B\hat{i}+B\hat{j}-B\hat{k}$
Magnitude of resultant field is
$|B_{net}|=\sqrt{B^2+B^2+B^2=}\sqrt{3}.B$