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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Warm-Up: Prerequisite Review

These questions review concepts needed for this section.

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

The same thing as Coulomb's force — they are identical.

The influence of a source charge on the space around it, independent of what test charge is placed there.

The force between two charges when one of them is very small.

The total force on all charges in a region.

A $+5 \times 10^{-6}$ 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.

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

toward the source charge

away from the source charge

perpendicular to the line connecting source to that point

in the direction of the nearest negative charge

Fluency Practice

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

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

No — there is no second charge to exert force on, so there is no field.

Yes — the electric field exists in space due to the source charge, whether or not a test charge is present.

Yes — but only along the line connecting the charge to that point.

No — the electric field requires at least two charges.

A point charge of $q = -8.0 \times 10^{-9}$ 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.

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

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

A positive charge to the right of the point

A negative charge to the right of the point

A positive charge to the left of the point

A negative charge to the left of the point

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

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

Diagram A — straight lines radiating outward

Diagram B — lines converging inward

Diagram C — spiraling lines

Diagram D — parallel lines

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?

The artist drew more lines close to the charge by mistake.

The field is stronger near the charge — field line density is proportional to field strength.

More lines were generated near the charge because it is a larger charge.

The field becomes negative as you move away, so fewer lines are drawn.

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

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

In the $+x$ direction (same as $E$ )

In the $-x$ direction (opposite to $E$ )

No force — the electron is neutral.

Perpendicular to the field.

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