A particle of charge ‘ q ’ and mass ‘ m ’ is projected from the origin with velocity u 0 i ^ + v 0 j ^ in a gravity free region where uniform electric field - E 0 i ^ and uniform magnetic field - B 0 i ^ exist. Find the condition so that the particle would return to origin at least for once.

Time for one complete rotation T 0 = 2 π m q B 0 Time for retracing motion in x direction T 1 = 2 u 0 m q E 0 ∴ T 1 T 0 must be an integer. So, 2 u 0 m q E 0 × q B 0 2 π m = u 0 B 0 π E 0

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Physics - Magnetism Question with Solution | TestHub

PhysicsMagnetismMagnetic ForceEasy2 minPYQ_2020

PhysicsEasysingle choice

A particle of charge ‘ $q$ ’ and mass ‘ $m$ ’ is projected from the origin with velocity $(u_{0} \hat{i} + v_{0} \hat{j})$ in a gravity free region where uniform electric field $- E_{0} \hat{i}$ and uniform magnetic field $- B_{0} \hat{i}$ exist. Find the condition so that the particle would return to origin at least for once.

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Answer:

Solution:

Time for one complete rotation $T_{0} = \frac{2 π m}{q B_{0}}$
Time for retracing motion in $x$ direction $T_{1} = \frac{2 u_{0} m}{q E_{0}}$
$∴ \frac{T_{1}}{T_{0}}$ must be an integer. So, $\frac{2 u_{0} m}{q E_{0}} \times \frac{q B_{0}}{2 π m} = \frac{u_{0} B_{0}}{π E_{0}}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:MagnetismSubtopic:Magnetic Force

⏱ 2mℹ️ Source: PYQ_2020

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