Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

The ratio of the radii of two circular coils is 1:2. The ratio of currents in the respective coils such that the same magnetic moment is produced at the centre of each coil is:

4:1

2:1

1:2

1:4

Step-by-Step Solution

Identify Formula: The magnetic dipole moment ( $M$ ) of a current-carrying circular coil is given by $M = N I A$ , where $N$ is the number of turns, $I$ is the current, and $A$ is the area of the coil.
Analyze Area: The area of a circle is $A = \pi r^2$ . Thus, $M = N I (\pi r^2)$ .
Set Condition: The problem states that the magnetic moments are the same ( $M_1 = M_2$ ) and implies single-turn coils or equal turns ( $N_1 = N_2$ ) as specific numbers aren't given. $I_1 \pi r_1^2 = I_2 \pi r_2^2$
Calculate Ratio: Rearrange to find the ratio of currents ( $I_1 / I_2$ ): $\frac{I_1}{I_2} = \frac{r_2^2}{r_1^2} = \left( \frac{r_2}{r_1} \right)^2$
Substitute Values: Given the ratio of radii $r_1 : r_2 = 1 : 2$ , implies $r_2 / r_1 = 2 / 1 = 2$ . $\frac{I_1}{I_2} = (2)^2 = 4$
Conclusion: The ratio of the currents is 4:1.

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