A particle of mass m and charge q is released from rest in a uniform electric field Find the momentum attained by the particle after moving distance xis

Momentum = 2qEx/v

Explanation:

From the work - energy theorem, we know that;

Kinetic energy = work done

Now, formula for both are;

Kinetic energy = ½mv²

Work done = qEx

Where;

m is mass

v is velocity

q is charge

E is Electric field

x is distance covered.

Thus;

½mv² = qEx - - - - (eq 1)

Now, momentum formula is;

p = mv

Let's rewrite the left hand side of equation 1 to reflect p = mv. Thus;

½v(mv) = qEx

½vp = qEx

p = 2qEx/v

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