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Chapter 17: Problem 15

A point charge \(q=+3.0\) nC moves through a potential difference $\Delta V=V_{\mathrm{f}}-V_{\mathrm{i}}=+25 \mathrm{V} .$ What is the change in the electric potential energy?

Short Answer

Expert verified
Answer: The change in electric potential energy of the point charge is 75 nJ.

Step by step solution

01

Identify the given information

The charge is \(q = 3.0 \times 10^{-9} \mathrm{C}\), and the potential difference is \(\Delta V = +25 \mathrm{V}\).
02

Use the electric potential energy formula

The formula for change in electric potential energy is \(U = q \times \Delta V\). Plug in the given values to calculate the change in electric potential energy.
03

Calculate the change in electric potential energy

Substitute the values of charge and potential difference in the formula: \(U = (3.0 \times 10^{-9} \mathrm{C}) \times (+25 \mathrm{V}) = 75 \times 10^{-9} \mathrm{J}\).
04

Convert the result to the appropriate unit

The electric potential energy is calculated in joules (J). Since the result is \(75 \times 10^{-9} \mathrm{J}\), we can convert it to nanojoules (nJ) by multiplying the value by \(10^9\). So, \(75 \times 10^{-9} \mathrm{J} = 75\) nJ.
05

Conclusion

The change in electric potential energy of the point charge is 75 nJ.

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Most popular questions from this chapter

A parallel plate capacitor has a capacitance of \(1.20 \mathrm{nF}\) There is a charge of \(0.80 \mu \mathrm{C}\) on each plate. How much work must be done by an external agent to double the plate separation while keeping the charge constant?
A point charge \(q=-2.5 \mathrm{nC}\) is initially at rest adjacent to the negative plate of a capacitor. The charge per unit area on the plates is $4.0 \mu \mathrm{C} / \mathrm{m}^{2}\( and the space between the plates is \)6.0 \mathrm{mm} .$ (a) What is the potential difference between the plates? (b) What is the kinetic energy of the point charge just before it hits the positive plate, assuming no other forces act on it?
A certain capacitor stores \(450 \mathrm{J}\) of energy when it holds $8.0 \times 10^{-2} \mathrm{C}$ of charge. What is (a) the capacitance of this capacitor and (b) the potential difference across the plates?
A hydrogen atom has a single proton at its center and a single electron at a distance of approximately \(0.0529 \mathrm{nm}\) from the proton. (a) What is the electric potential energy in joules? (b) What is the significance of the sign of the answer?
(a) If the bottom of a thundercloud has a potential of $-1.00 \times 10^{9} \mathrm{V}\( with respect to Earth and a charge of \)-20.0 \mathrm{C}$ is discharged from the cloud to Earth during a lightning strike, how much electric potential energy is released? (Assume that the system acts like a capacitoras charge flows, the potential difference decreases to zero.) (b) If a tree is struck by the lightning bolt and \(10.0 \%\) of the energy released vaporizes sap in the tree, about how much sap is vaporized? (Assume the sap to have the same latent heat as water.) (c) If \(10.0 \%\) of the energy released from the lightning strike could be stored and used by a homeowner who uses \(400.0 \mathrm{kW}\). hr of electricity per month, for how long could the lightning bolt supply electricity to the home?
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