Practice portal › Electric Charge and Properties › Motion of a Charge in an Electric Field

A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (the graphs are schematic and not drawn to scale)

Asked in JEE Main 8th Jan 2nd Shift 2020 · Deflection and projectile motion

• (1) v grows linearly with x (a straight line through the origin)
• (2) v grows with x along a curve bending steeply upwards (concave up)
• (3) v grows with x along a curve that rises steeply at first and then flattens (concave down, v∝√x)
• (4) v stays near zero at first and then rises in an S-shaped curve

Step-by-step solution

Why the other options are wrong

• (1) Confuses the v-t graph with the v-x graph; v is linear in TIME, not in distance.
• (2) Would require v to grow faster than x, i.e. the acceleration to increase, but the field and hence the acceleration are constant.
• (4) An S-shape needs the acceleration first to grow and then to fall; a uniform field gives one fixed acceleration throughout.

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.