Electric potential energy for a charge in a uniform electric field (17-2)
Question
The change in electric potential energy for an object of charge \(q\) that moves in a uniform electric field \(\vec{E}\)...
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Review
This analogy between gravitational force and electric force tells us how to write the change in electric potential energy for an object of charge \(q\) that undergoes a displacement \(\vec{d}\) in the presence of a uniform electric field \(\vec{E}\) (Figure 17-3a). Following the same steps that we used to find Equation 17-1 above, you can see that if \(\theta\) is the angle between the directions of \(\vec{d}\) and \(\vec{E}\), then the work done on the charge by the electric force \(\vec{F} = q\vec{E}\) is \(W_{\mathrm{electric}} = qEd \cos{\theta}\). The change in electric potential energy equals the negative of the electric work done on the charge:
