A particle having mass m and charge q is at rest. On applying a uniform electric field E on it, it starts moving. What is its kinetic energy when it travels a distance y in the direction of the force?

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(3) qEy. Given: the particle starts from rest, and the field is uniform, so the force on it, F=qE, is constant. Idea: work-energy theorem — the kinetic energy gained equals the work done by the electric force. Work over a displacement y along the force: W=Fy=qEy. The same result in potential language: the particle falls through a potential difference Δ V=Ey, and W=q Δ V. Starting from rest, K=W=qEy. The mass does not appear — it decides how fast the particle ends up moving, not how much energy it gains.

A particle having mass m and charge q is at rest. On applying a uniform electric field E on it, it starts moving. What is its kinetic energy when it travels a distance y in the direction of the force?

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