Moving Charges and Magnetism - Result Question 41
42. Two circular coils 1 and 2 are made from the same wire but the radius of the $1^{\text{st }}$ coil is twice that of the $2^{\text{nd }}$ coil. What potential difference in volts should be applied across them so that the magnetic field at their centres is the same
(a) 4
(b) 6
(c) 2
(d) 3
[2006]
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Answer:
Correct Answer: 42. (None)
Solution:
- (None) If $R_1 & R_2$ be the radius of the circular wires, $\frac{R_1}{R_2}=\frac{2}{1}$. If same potential is applied on them, current in Ist will be half that in the later. If $V$ potential is applied on them, current in them $=\frac{V}{2 R} & \frac{V}{R}$.
Now magnetic field at the centre of circular
coil, $=\frac{\mu_0 I}{2 r}$
For first wire, field $B_1=\frac{\mu_0 V}{2 R \times 2 R}$
For second wire, field $B_2=\frac{\mu_0 V}{2(R / 2) \times R}$
Given $B_1=B_2$
The given data do not provide any required result. There is a mistake in the framing of the question.
