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 :

• A. $P$ only
• B. $P$ and $Q$ only
• C. $Q$ and $R$ only
• D. $P$ and $R$ only

Answer 1

Answer: (C)

$Q$ and $R$ only

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 $R_{thick}$ and resistance of thin wire be $R_{thin}$
$R=\frac{\rho l}{A}$ where $l$ is the length$,A$ is the cross section area and $\rho$ is the resistivity.
$R_{thick}<R_{thin}$ since $A_{thick}>A_{thin}$

$CaseP:$
Current in thick sections of wire will be different from that in thin sections since resistances are $2R_{thick}$ and $2R_{thin}$ and are different.
$\therefore$ magnetic field produced by thick wires will not cancel that due to thin wires.

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

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