A cool easy problem 9

Electricity and Magnetism Level 2

In the electric field of charge q , another charge is taken from A to B , A to C , A to D and A to E , then the work done will be?

minimum along AC equal along AB and AE cannot say till charge at A is not known minimum along AD zero along all the path

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3 solutions

Gagan Raj
Mar 17, 2015

Electric Field is a conservative field which means it is independent of the path taken. Hence , the work done too will be zero along any path.

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Nikhil Jaiswal
Apr 3, 2015

we can say a,b,c,d,e lie on a equipotential surface work done = q*delta v so zero work done

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Caleb Townsend
Feb 9, 2015

The work done by the field is W = F ⃗ ⋅ Δ x ⃗ W = \vec{F} \cdot \Delta \vec{x} As we can see in the diagram, F ⃗ \vec{F} is orthogonal (perpendicular) to Δ x ⃗ \Delta \vec{x} for every given path. Therefore, the dot product is 0 0 , i.e. W = F ⃗ ⋅ Δ x ⃗ = 0 W = \vec{F} \cdot \Delta \vec{x} = \boxed{0}

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