In a certain region of space, there exists a uniform and constant electric field of strength E along $$x-axis$$ and uniform constant magnetic field of induction B along $$z-axis$$. A charged particle having charge q and mass m is projected with speed v parallel to $$x-axis$$ from a point (a$$, b, $$0). When the particle reaches a point $$2a$$, $$b2$$, $$0$$ its speed becomes $$2v$$. Find the value of electric field strength.

Question

In a certain region of space, there exists a uniform and constant electric field of strength E along $$x-axis$$ and uniform constant magnetic field of induction B along $$z-axis$$. A charged particle having charge q and mass m is projected with speed v parallel to $$x-axis$$ from a point (a$$, b, $$0). When the particle reaches a point $$2a$$,   $$b2$$,  $$0$$ its speed becomes $$2v$$. Find the value of electric field strength.

Infinity Learn · Accepted Answer

Change in kinetic energy is only due to work done by electric field. Hence, work done by electric field is change in $$KE$$.qEa $$=12$$ m  $$2v2$$−$$v2$$ ⇒  $$E=3mv22qa$$

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