Physics Q41 – JEE-MAIN 2026

Home Physics Moving ChargesQuestion #345

An insulated wire is wound so that it forms a flat coil with

N = 200

turns. The radius of the innermost turn is

r_{1} = 3

cm, and of the outermost turn

r_{2} = 6

cm. If

20

mA current flows in it then the magnetic moment will be

α \times 10^{- 2}

A.m

^{2}

. The value of

α

is _______.

Clue 1 of 3: Conceptual Principle

The magnetic moment of a current-carrying coil depends on the current, the number of turns, and the area enclosed by the turns.

🧠 Full Solution Path

Step 1: Identify the formula for magnetic moment of a flat spiral coil✦ Active

For a flat spiral coil with $N$ turns uniformly distributed between an inner radius $r_{1}$ and an outer radius $r_{2}$ , carrying a current $I$ , the magnetic moment $M$ is given by:

M = \frac{I N π}{3} (r_{1}^{2} + r_{1} r_{2} + r_{2}^{2})

Step 2: Substitute given values and calculate the magnetic moment○ Expand

Given values are: $N = 200$ turns, $r_{1} = 3 cm = 0.03 m$ , $r_{2} = 6 cm = 0.06 m$ , and $I = 20 mA = 20 \times 10^{- 3} A$ . Substitute these into the formula:

M = \frac{(20 \times 10^{- 3} A) (200) π}{3} ((0.03 m)^{2} + (0.03 m) (0.06 m) + (0.06 m)^{2})

M = \frac{4 π}{3} (0.0009 + 0.0018 + 0.0036)

M = \frac{4 π}{3} (0.0063) = 4 π (0.0021) = 0.0084 π {A.m}^{2}

💡 Teacher's Secret Hint

Ensure all units are converted to SI units before calculation to avoid errors.

Step 3: Determine the value of

α

○ Expand

Using the approximation $π \approx 3.14159$ , the magnetic moment is:

M \approx 0.0084 \times 3.14159 \approx 0.026389 {A.m}^{2}

The problem states that the magnetic moment is $α \times 10^{- 2} {A.m}^{2}$ . Therefore:

α \times 10^{- 2} = 0.026389

α = \frac{0.026389}{10^{- 2}} = 2.6389

Rounding to two decimal places, $α \approx 2.64$ . This corresponds to option 2.

💡 Teacher's Secret Hint

Pay attention to the required format of the final answer, specifically the power of 10.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 41 – JEE-MAIN 2026

Clue 1 of 3: Conceptual Principle

🧠 Full Solution Path