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Back to Exercise: Electric Field

Exercises: Electric Field

Work through each section in order. Use $k = 9 \times 10^9$ N·m²/C² throughout. Show your work on calculation problems.

Grade 11·22 problems·~35 min·OpenStax Physics (High School)·section·sec-18-3
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A

Warm-Up: Prerequisite Review

These questions review concepts needed for this section.

1.

Coulomb's Law gives the force between two specific charges. What is the electric field concept designed to describe?

2.

A +5×10−6+5 \times 10^{-6} C charge is located at the origin. What is the magnitude of the electric field at a distance of 0.30 m from this charge? Express your answer in N/C to two significant figures.

3.

The electric field at a point due to a positive source charge points —

B

Fluency Practice

Use k=9×109k = 9 \times 10^9 N·m²/C². Show your work on calculation problems.

1.

A charge of +3+3 μC is fixed in space. No other charges are present. Does an electric field exist at a point 0.5 m away?

2.

A point charge of q=−8.0×10−9q = -8.0 \times 10^{-9} C is at the origin. What is the magnitude of the electric field at a point 0.40 m away? Express your answer in N/C to two significant figures.

3.

A test charge of q0=+2.0×10−9q_0 = +2.0 \times 10^{-9} C is placed at a point where the electric field has magnitude E=3.0×104E = 3.0 \times 10^4 N/C. What is the magnitude of the force on the test charge? Express your answer in newtons.

4.

At a point in space, the electric field points to the right (positive xx direction). Which source charge configuration could produce this field?

Four field line diagrams for a positive charge: A shows lines radiating outward, B shows lines converging inward, C shows spiraling lines, D shows parallel horizontal lines
5.

Which description correctly matches the electric field line pattern for an isolated positive charge?

6.

A field line diagram shows 8 lines near a charge and 2 lines far away from the same charge. What does this difference in density indicate?

Diagram of a uniform electric field pointing right with a proton and electron placed in it, showing unknown force directions on each
7.

A uniform electric field points in the +x+x direction. A proton (charge +e+e) and an electron (charge −e-e) are both placed in this field. What is the direction of the force on the electron?

C

Mixed Practice

These problems apply electric field concepts in varied formats.

1.

The electric field EE at a point in space has a specific value regardless of whether a test charge is placed there. Which statement best explains why the field concept is more powerful than the force concept?

2.

At a given point in space, the electric field has magnitude E=200E = 200 N/C pointing upward. A charge of q=−4.0×10−6q = -4.0 \times 10^{-6} C is placed at that point. In two to three sentences, state the direction of the force on this charge and explain why it differs from the field direction. Include the calculated magnitude of the force.

Electric field line diagram showing a positive and negative charge with field lines curving from the positive charge to the negative charge
3.

In a field line diagram of two opposite charges (a positive and a negative charge separated by some distance), which description is correct?

4.

Two identical positive charges are placed near each other. Which description correctly characterizes their combined field line pattern?

5.

In a field line diagram of a single isolated charge, the lines are much closer together near the charge than far away. What does this tell us?

D

Application Problems

Read each scenario carefully. Show your work on calculations.

1.

A point charge of q=+6.0×10−9q = +6.0 \times 10^{-9} C is fixed at the origin. A small test charge of q0=−3.0×10−9q_0 = -3.0 \times 10^{-9} C is placed at a distance of r=0.20r = 0.20 m from the source charge.

1.

What is the magnitude of the electric field at the location of the test charge (due to the source charge only)? Express your answer in N/C to two significant figures.

2.

What is the magnitude of the electric force on the test charge? Express your answer in newtons to two significant figures.

2.

Two parallel metal plates create a uniform electric field of E=500E = 500 N/C pointing from the top plate (positive) to the bottom plate (negative). An electron (charge −e=−1.6×10−19-e = -1.6 \times 10^{-19} C) is released from rest between the plates.

In which direction does the electron accelerate?

3.

An electric field of E=8.0×103E = 8.0 \times 10^3 N/C points horizontally to the right. A particle with charge q=−5.0×10−6q = -5.0 \times 10^{-6} C is placed in this field.

What is the magnitude of the force on the particle? Express your answer in newtons.

E

Find the Mistake

Each problem shows incorrect reasoning. Identify the error.

1.

A student writes: "The electric field at a point is E=500E = 500 N/C. This means there must be a test charge of 1 C at that point experiencing 500 N of force."

What is the conceptual error in this statement?

2.

A student looks at a field line diagram for a single positive charge and says: "The field lines show the path the positive charge will travel — it will spiral outward from itself."

What is wrong with the student's interpretation of field lines?

F

Challenge Problem

This bonus problem requires multi-step reasoning.

1.

Two point charges are on a line: q1=+4.0×10−9q_1 = +4.0 \times 10^{-9} C at x=0x = 0 and q2=−4.0×10−9q_2 = -4.0 \times 10^{-9} C at x=0.10x = 0.10 m. Find the magnitude of the net electric field at the midpoint (x=0.05x = 0.05 m).

What is the magnitude of the net electric field at the midpoint? Express your answer in N/C. (Both field contributions point in the same direction at the midpoint — find each one and add them.)

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