Electric Potential and Potential Difference
3.2 Electric Potential and Potential Difference
Learning Objectives
By the end of this section, you will be able to:
- Define electric potential, voltage, and potential difference
- Define the electron-volt
- Calculate electric potential and potential difference from potential energy and electric field
- Describe systems in which the electron-volt is a useful unit
- Apply conservation of energy to electric systems
Electric Potential Difference
Practice!
| Practice 3.2.1 |
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| An electron is pushed into an electric field where it acquires a 1 V electrical potential. Suppose instead that two electrons are pushed the same distance into the same electric field. The electrical potential acquired by the two electrons is … ? |
| Practice 3.2.2 |
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Two test charges are brought separately into the vicinity of a charge +Q. First, test charge +q is brought to point A a distance r from +Q. Next, +q is removed and a test charge +2q is brought to point B a distance 2r from +Q. Compared with the electrostatic potential of the charge at A, the electrostatic potential of the charge at B is … ? |
| Pause & Predict 3.2.1 |
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| What is the electric field between the cathode and the anode? |
| Pause & Predict 3.2.2 |
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| What is the electric potential 0.25 cm from the cathode? |
Practice!
| Practice 3.2.3 |
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 In a region where there is a uniform electric field, the potential, V1, is 1.3 V at position y1 = 26 cm. At position y2 = 28 cm, the potential, V2, is 3.9 V. What is the magnitude of the y-component of the electric field in this region? |
| Practice 3.2.4 |
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In a region where there is a uniform electric field, the potential, V1, is 1.3 V at position y1 = 26 cm. At position y2 = 28 cm, the potential, V2, is 3.9 V. What is the potential at position y3 = 32 cm? |
| Practice 3.2.5 |
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In a region where there is a uniform electric field, the potential, V1, is 1.3 V at position y1 = 26 cm. At position y2 = 28 cm, the potential, V2, is 3.9 V. What is the change in electric potential energy of an alpha particle (charge = +2e) if it is moved from y1 to y3? |
Discuss!
Reflect on this question and take notes on how you would answer it. Then we will share these thoughts together in a class discussion.
Before the advent of solid-state electronics, vacuum tubes were widely used in radios and other devices. A simple type of vacuum tube known as a diode consists essentially of two electrodes within a highly evacuated enclosure. One electrode, the cathode, is maintained at a high temperature and emits electrons from its surface. A potential difference of a few hundred volts is maintained between the cathode and the other electrode, known as the anode, with the anode at the higher potential.
Suppose a diode consists of a cylindrical cathode with a radius of 6.200 × 10−2 cm, mounted coaxially within a cylindrical anode with a radius of 0.5580 cm. The potential difference between the anode and cathode is 245 V. An electron leaves the surface of the cathode with zero initial speed (vinitial = 0). Find its speed vfinal when it strikes the anode.
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