The electric potential at the origin of an xy-coordinate system is 40 v. a -8.0-μc charge is brought from x = +∞ to that point. what is the electric potential energy of this charge at the origin?

-320 μJ.

Explanation:

Consider a point with an electrical charge of . Assume that is the electrical potential at the position of that charge. The electrical potential of that point charge will be equal to:

.

Keep in mind that since both and might not be positive, the size of the electrical potential energy might not be positive, either.

For this point charge,

Hence its electrical potential energy:

.

Why is this value negative? The electrical potential energy of a charge is equal to the work needed to bring that charge from infinitely far away all the way to its current position. Also, negative charges are attracted towards regions of high electrical potential. Bringing this negative charge to the origin will not require any external work. Instead, this process will release 320 μJ of energy. As a result, the electrical potential energy is a negative value.

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energy stored in the capacitor= 9.72 x 10⁻⁴ j

explanation:

the energy stored in the capacitor is given by

e= 1/2 c v²

e= energy stored

c= capacitance= 1.5 µc= 1.5 x 10⁻⁶f

v= potential difference=36 v

so energy stored= e= 1/2 (1.5 x 10⁻⁶) (36)²

energy stored= 9.72 x 10⁻⁴j