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Question

There is a uniform electric field of strength of 103Vm-1 along the y−axis. A body of mass 1g and charge 10-6C is projected into the field from the origin along the positivex−axis with a velocity of 10m/s. Find its speed in m/s after 10sec is (neglect gravitation).


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Solution

Step 1: Given parameters.

Velocity in x-direction, Vx=10m/s

Electric field, E=103V/m

Charge, q=10-6C

Mass, m=1g

Step 2: Calculate the speed of body after 10sec.

As velocity in the x-direction remains constant at 10m/s

Now, the acceleration will be in the y-direction only,

a=qEm...1

where, a is the acceleration of the body, q is the charge of the body, Eis the electric field and, m is the mass of the body.

Substitute the given values in equation (1).

a=10-6×1031×10-3

a=1m/s2

The velocity in the y-direction will be,

Vy=a×t

Vy=1×10

Vy=10m/s

Therefore the final velocity of the body,

V=10x^+10y^

|V|=102m/s

Hence, the speed of the body after 10sec will be 102m/s.


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