Question

Two circular coils of wires made of wire of same gauge have the same number of turns and have radii 20 cm and 40 cm. They are connected in parallel to a battery. The ratio of the magnetic inductions at the centers of the coils is:

• A. 1 : 2
• B. 2 : 1
• C. 1 : 4
• D. 4 : 1

Answer 1

The correct option is D 4 : 1

Resistance$\alpha$ l
$\therefore R_1=R$
& $R_2=2R$
Current in coil 1$=\frac{V}{R}=i$
Current in coil 2$=\frac{V}{2R}=\frac{i}{2}$
$B_1=\frac{{\mu }_{0}i}{2R}=\frac{{\mu }_{0}i}{2R}$
$B_2=\frac{{\mu }_0{i}_2}{4R}=\frac{{\mu }_{0}i}{8R}$
$B_1:B_2=4:1$