A particle of mass $$2$$ x $$105$$ kg moves horizontally between two horizontal plates of a charged parallel plate capacitor between which there is an electric field of $$200$$ $$NC-1$$ acting upward. A magnetic induction of $$2.0$$ T is applied at right angles to the electric field in a direction normal to both B→ and v→. If g is $$9.8$$ m $$s-2$$ and the charge on the particle is $$10-6$$ C, then find the velocity of charge particle so that it continues to move horizontally

Question

A particle of mass $$2$$ x $$105$$ kg moves horizontally between two horizontal plates of a charged parallel plate capacitor between which there is an electric field of $$200$$ $$NC-1$$ acting upward. A magnetic induction of $$2.0$$ T is applied at right angles to the electric field in a direction normal to both B→ and v→. If g is $$9.8$$ m $$s-2$$ and the charge on the particle is $$10-6$$ C, then find the velocity of charge particle so that it continues to move horizontally

Infinity Learn · Accepted Answer

Net force on the particle should be zero.$$qE=10-6$$×$$200=2$$×$$10-4$$ $$Nmg=2$$×$$10-5$$×$$9.8=1.96$$×$$10-4$$ NSince qE > mg, so magnetic forc e qvB should act downward to balance the $$forcesqE=mg+qvB$$⇒$$2$$×$$10-4=1.96$$×$$10-4+10-6v$$×$$2$$ ⇒  $$v=2$$ $$m/s$$

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