The electric field acts along positive $$x-axis$$. A charged particle of charge q and mass m is released from origin and moves with velocity v→$$=v0j^$$ under the action of electric field and magnetic field, B→$$=B0i^$$ The velocity of particle becomes $$2v0$$ after time $$3$$ $$mv02$$ $$qE0$$. Find the electric field.

Question

The electric field acts along positive $$x-axis$$. A charged particle of charge q and mass m is released from origin and moves with velocity v→$$=v0j^$$ under the action of electric field and magnetic field, B→$$=B0i^$$ The velocity of particle becomes $$2v0$$ after time $$3$$ $$mv02$$ $$qE0$$.  Find the electric field.

Infinity Learn · Accepted Answer

v→ is perpendicular to both E→ and B→.Path of particle is helix with increasing $$pitchv=vx2$$  $$+$$  $$vy2$$  $$+$$  $$vz21/2Here$$,   $$vx2=qEmt2$$  and  $$vy2$$  $$+$$  $$vz2$$  $$=$$  $$v02Also$$,  $$v=2v02v02$$  $$=$$  $$q2E2t2m2$$ $$+$$  $$v02t=$$ $$3$$  $$mv0qE$$  $$=$$ $$3$$  $$mv03qE0$$       givenE→$$=2$$ $$E0i^$$

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The electric field acts along positive x-axis. A charged particle of charge q and mass m is released from origin and moves with velocity v→=v0j^ under the action of electric field and magnetic field, B→=B0i^ The velocity of particle becomes 2v0 after time 3 mv02 qE0. Find the electric field.

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