JEE Main · 2020 · 06 Sep 2020 · Shift 1 · Magnetic Effects of Current

A particle of charge

q

and mass

m

is moving with a velocity

- v \hat{i} (v \neq = 0)

towards a large screen placed in the

Y - Z

plane at a distance

d

. If there is a magnetic field

B = B_{0} \hat{k}

, the maximum value of

v

for which the particle will not hit the screen is:

(A) $\frac{qdB _{0}}{3 m}$
(B) $\frac{2 q d B _{0}}{m}$
(C) $\frac{qdB _{0}}{m}$ ✓ Correct
(D) $\frac{qdB _{0}}{2 m}$

Answer: (C)

Solution

In the field

B = B_{0} \hat{k}

the particle, entering along

- \hat{i}

, travels on a circular arc of radius

r = \frac{m v}{q B _{0}}

. Entering perpendicular to the screen, it penetrates towards the screen by at most one radius before the magnetic force curves it back. It just fails to reach the screen a distance

d

away when this greatest penetration equals

d

, i.e.

\frac{m v}{q B _{0}} = d

, which fixes the threshold speed

v = \frac{q B _{0} d}{m}

JEE Main · 2020 · 06 Sep 2020 · Shift 1 · Single correct option

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JEE Main · 2020 · 06 Sep 2020 · Shift 1 · Magnetic Effects of Current

Solution

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