A uniform electric field is parallel to the x axis. In what direction can a charge be displaced in this field without any external work being done on the charge?

θ=π/2

Explanation:

The definition of work is W = → F ⋅ → d = q E c o s θ d W=F→⋅d→=qEcosθd. So if no work is done, the displacement must be in the direction perpendicular to the force ie c o s θ = 0 → θ = π / 2 cosθ=0→θ=π/2

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