Q71 / 91 · KVPY 2018 (SB/SX) · Physics

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.

Figure
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 centre will be

  • A
    zero
  • B
    2B
  • Correct answer
    C
    3B
  • D
    B

Solution

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

Figure

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

Figure

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

Figure

∴Bnet=Bi^+Bj^-Bk^

Magnitude of resultant field is

Bnet=B2+B2+B2=3·B

Hence, the correct answer is option: 'C'.

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