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At a certain point in space, there is a potential of 800 V relative to zero. What is the potential energy of the system when a +1.0 μC charge is placed at that point in space?

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To solve this problem we will apply the concepts related to electric potential and electric potential energy. By definition we know that the electric potential is determined under the function:


V = (k_e q)/(r)


k_e = Coulomb's constant

q = Charge

r = Radius

At the same time


U = (k_e q_1q_2)/(r)

The values of variables are the same, then if we replace in a single equation we have this expression,


U = Vq

If we replace the values, we have finally that the charge is,


V = 800V


q = 1\mu C


U = (800V)(1*10^(-6)C)


U = 8*10^(-4)J

Therefore the potential energy of the system is
8*10^(-4) J

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