PHYS 2212 Module 3.4

Determining Field from Potential

Recommended Reading

3.4 Determining Field from Potential

Learning Objectives

By the end of this section, you will be able to:

  • Explain how to calculate the electric field in a system from the given potential
  • Calculate the electric field in a given direction from a given potential
  • Calculate the electric field throughout space from a given potential

Relating Electric Field and Electric Potential

The electric field is equal to the negative gradient of the electric potential:

where the del operator is:


Practice 3.4.1
Two points A and B are located within a region in which there is an electric field.

How would you describe the potential difference ∆V = VB − VA?
Check your answer: B. It is negative
Practice 3.4.2
A proton is placed at position P on the x axis where the potential is -10V.

Which of the following statements is true?
Check your answer: D. The motion cannot be predicted.
Practice 3.4.3
A proton is released from rest at point B, where the potential is 0 V.

Afterward, the proton … ?
Check your answer: A. moves toward A with an increasing speed.
Practice 3.4.4
In a certain region of space, the electric potential is +2 V everywhere along the x axis. From this information, you can conclude that the x component of the electric field in this region:
Check your answer: A. is zero