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Chapter 17: Problem 90

If an electron moves from one point at a potential of \(-100.0 \mathrm{V}\) to another point at a potential of \(+100.0 \mathrm{V}\) how much work is done by the electric field?

Short Answer

Expert verified
Answer: The work done by the electric field on the electron is \(-3.2 \times 10^{-17} \, \mathrm{J}\).

Step by step solution

01

Write down the given information

We are given the initial electric potential, \(V_i = -100.0 \mathrm{V}\), and the final electric potential, \(V_f = +100.0 \mathrm{V}\). We need to find out the work done by the electric field (\(W\)).
02

Write down the formula to calculate the work done by the electric field

According to the work-energy theorem, the work done by the electric field is equal to the change in the electron's potential energy. The formula for the work done by the electric field is: $$W = q \Delta V$$ where \(q\) is the charge of the electron and \(\Delta V\) is the change in electric potential.
03

Calculate the change in electric potential

The change in electric potential is the final electric potential minus the initial electric potential: $$\Delta V = V_f - V_i$$ Substitute the given values into the equation: $$\Delta V = (+100.0 \mathrm{V}) - (-100.0 \mathrm{V}) = 200.0 \mathrm{V}$$
04

Identify the charge of the electron

The charge of the electron, \(q\), is a known constant value: $$q = -1.6 \times 10^{-19} \, \mathrm{C}$$ Note that the charge is negative, as electrons are negatively charged particles.
05

Calculate the work done by the electric field

Using the formula from Step 2, substitute the values for \(q\) and \(\Delta V\) to find the work done by the electric field: $$W = q \Delta V$$ $$W = (-1.6 \times 10^{-19} \, \mathrm{C}) (200.0 \mathrm{V})$$ Calculate the work: $$W = -3.2 \times 10^{-17} \, \mathrm{J}$$ So, the work done by the electric field on the electron is \(-3.2 \times 10^{-17} \, \mathrm{J}\).

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Most popular questions from this chapter

It is believed that a large electric fish known as Torpedo occidentalis uses electricity to shock its victims. A typical fish can deliver a potential difference of \(0.20 \mathrm{kV}\) for a duration of \(1.5 \mathrm{ms}\). This pulse delivers charge at a rate of \(18 \mathrm{C} / \mathrm{s} .\) (a) What is the rate at which work is done by the electric organs during a pulse? (b) What is the total amount of work done during one pulse?
A parallel plate capacitor has a charge of \(0.020 \mu \mathrm{C}\) on each plate with a potential difference of \(240 \mathrm{V}\). The parallel plates are separated by 0.40 mm of air. What energy is stored in this capacitor?
A parallel plate capacitor is attached to a battery that supplies a constant voltage. While the battery is still attached, a dielectric of dielectric constant \(\kappa=3.0\) is inserted so that it just fits between the plates. What is the energy stored in the capacitor after the dielectric is inserted in terms of the energy \(U_{0}\) before the dielectric was inserted?
A spherical conductor with a radius of \(75.0 \mathrm{cm}\) has an electric field of magnitude \(8.40 \times 10^{5} \mathrm{V} / \mathrm{m}\) just outside its surface. What is the electric potential just outside the surface, assuming the potential is zero far away from the conductor?
(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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