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Question

Two thick wires and two thin wires, all of the same materials and same length, form a square in three different ways P, Q and R as shown in the figure. With correct connections shown, the magnetic field at the centre of the square is zero in case of :
143660.png
  1. P and Q only
  2. Q and R only
  3. P only
  4. P and R only

A
P only
B
Q and R only
C
P and Q only
D
P and R only
Solution
Verified by Toppr

Magnetic field at the center will be due to the four finite wires in each of the cases P, Q and R.
Let the resistance of thick wire be Rthick and resistance of thin wire be Rthin
R=ρlA where l is the length, A is the cross section area and ρ is the resistivity.
Rthick<Rthin since Athick>Athin

Case P:
Current in thick sections of wire will be different from that in thin sections since resistances are 2Rthick and 2Rthin and are different.
magnetic field produced by thick wires will not cancel that due to thin wires.

Case Q:
Resistance of length CID is equal to resistance of CJD.
Hence, both will have the same current.
magnetic fields due to CID and CJD will cancel each other.

Case R:
Resistance of length EKF is equal to resistance of ELF.
Hence, both will have the same current.
magnetic fields due to EKF and ELF will cancel each other.

197725_143660_ans.png

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