Question

A circular conducting wire having uniform resistance per unit length is connected to a battery of $4V$. The total resistance of the conductor is $4\Omega$. Then the net magnetic field at the centre of the conductor is (Ignore magnetic field of wire present in circuit other than that of circular conducting wire)

• A. $\frac{{\mu }_0}{2}$
• B. $\frac{8{\mu }_0}{3}$
• C. $2{\mu }_0$
• D. Zero

Answer 1

The correct option is D Zero


Magnetic field due to a portion of circular conductor wire at centre $B_2=\frac{{\mu }_{0}I\theta }{4\pi R}$, where $\theta$ is angle subtended by centre due to portion of circular wire.
Since, resistance is directly proportional to length and inversely proportional to current, therefore
$\frac{I_1}{I_2}=\frac{l_2}{l_1}=3$
$B_1=\frac{{\mu }_0{I}_1}{4\pi R}\times \frac{\pi }{2}=\frac{{\mu }_{0}3I_2}{4\pi R}\times \frac{\pi }{2}$
$B_2=\frac{{\mu }_0{I}_2}{4R}\times \frac{3\pi }{2}$
$B_{net}=B_1-B_2=0$