Identifying the Electric Field Pattern for a Quadrupole

Q. What is the correct sketch of the weak electric field of a quadrupole (two positive and two negative charges)?

Background

Topic: Electric Field Patterns of Multipoles

This question tests your understanding of how electric field lines are arranged for a quadrupole configuration, which consists of two positive and two negative charges placed at the corners of a square.

Key Terms and Concepts:

• Quadrupole: A system of four charges arranged such that two are positive and two are negative, typically at the corners of a square.

• Electric Field Lines: Lines that represent the direction and strength of the electric field. They originate from positive charges and terminate on negative charges.

• Field Line Rules: Field lines never cross, and the density of lines indicates the field's strength.

Step-by-Step Guidance

1. Visualize the arrangement: Place two positive charges and two negative charges at the corners of a square, alternating in sign.

2. Recall that electric field lines start on positive charges and end on negative charges. For a quadrupole, lines will curve from each positive to each nearby negative.

3. Consider symmetry: The field pattern should be symmetric with respect to the center of the square and along its diagonals.

4. Look for a pattern where the field lines show the correct direction (from + to -) and the correct symmetry for a quadrupole.

Try solving on your own before revealing the answer!

Final Answer:

The correct sketch is the one where the field lines originate from the positive charges and terminate on the negative charges, forming a symmetric pattern characteristic of a quadrupole. The image above (image_1) accurately represents this configuration.

This pattern shows the field lines curving between adjacent positive and negative charges, with symmetry about the center and diagonals of the square.