A 5 mg particle carrying a charge of $5 \pi \times 10^{-6} \mathrm{C}$ is moving with velocity of $(3 \hat{\mathrm{i}}+2 \hat{\mathrm{k}}) \times 10^{-2} \mathrm{~m} / \mathrm{s}$ in a region having magnetic field $\overrightarrow{\mathrm{B}}=0.1 \hat{\mathrm{k}} \mathrm{Wb} / \mathrm{m}^{2}$. It moves a distance of $\alpha$ meter along $\hat{\mathrm{k}}$ when it completes 5 revolutions. The value of $\alpha$ is ______.

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Magnetic Effects of Current

A 5 mg particle carrying a charge of

5 π \times 1 0^{- 6} C

is moving with velocity of

(3 \hat{i} + 2 \hat{k}) \times 1 0^{- 2} m / s

in a region having magnetic field

B = 0.1 \hat{k} Wb / m^{2}

. It moves a distance of

α

meter along

\hat{k}

when it completes 5 revolutions. The value of

α

is ______.

Answer: 2

Solution

The velocity component along

\hat{k}

, parallel to

B

, is unaffected by the field and equals

v_{z} = 2 \times 1 0^{- 2} m/s

. One revolution takes

T = \frac{2 π m}{q B} = \frac{2 π ( 5 \times 1 0 ^{- 6} )}{( 5 π \times 1 0 ^{- 6} ) ( 0.1 )} = 20 s

. In five revolutions the elapsed time is

5 T = 100 s

, and the displacement along

\hat{k}

α = v_{z} \times 5 T = 2 \times 1 0^{- 2} \times 100 = 2 m

. The value of

α

2

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Integer answer

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