Electric Field Examples: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Electric Field.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

A region around a charged object where other charges experience a force. Measured in newtons per coulomb (N/C) or volts per meter (V/m).

Every charge creates an invisible 'force zone' around it. Another charge entering this zone feels a push or pull without touching anything.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Electric Field starts by naming the source, the object affected, and how the field or potential changes through space.

Common stuck point: Students often know a formula related to electric field but skip the recognition step: Am I using a field or potential to explain how one object influences another across space? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I using a field or potential to explain how one object influences another across space?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Coulomb's Law Mistakes

Worked Examples

Example 1

medium

What is the electric field

0.5 \text{ m}

from a point charge of

4 \times 10^{-6} \text{ C}

? Use

k = 9 \times 10^9 \text{ N m}^2/\text{C}^2

Answer

E = 1.44 \times 10^{5} N/C

First step

Electric field from a point charge:

E = k \frac{q}{r^{2}}

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Example 2

medium

A charge of

2 \times 10^{-9} \text{ C}

is placed in an electric field of

5000 \text{ N/C}

. What force does it experience?

A 2 nC charge in a 5000 N/C electric field; the net electric force is 10 μN in the field direction.

Example 3

medium

+5\ \mu\text{C}

point charge sits at the origin. Find the field magnitude at

r = 0.1\ \text{m}

. Use

k = 9\times10^9

Example 4

medium

Field

E_1 = 300\ \text{N/C}

points east and

E_2 = 400\ \text{N/C}

points north at a point. Find the magnitude of the net field.

Fields E₁ = 300 N/C (east) and E₂ = 400 N/C (north) combine by vector addition to give E_net = 500 N/C.

Example 5

hard

An electron is launched at

v_0 = 2.0\times10^6\ \text{m/s}

horizontally into a uniform downward field

E = 500\ \text{N/C}

. After

1.0\times10^{-8}\ \text{s}

, what is its vertical deflection? (

q = -1.6\times10^{-19}\ \text{C}

m = 9.11\times10^{-31}\ \text{kg}

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

hard

Two parallel plates are separated by

0.02 \text{ m}

with a potential difference of

100 \text{ V}

. What is the electric field between the plates?

Between two parallel plates 0.02 m apart with 100 V across them, the uniform field E = V/d

Example 2

hard

Two point charges are placed on the x-axis:

q_1 = +3 \times 10^{-6} \text{ C}

x = 0

and

q_2 = +3 \times 10^{-6} \text{ C}

x = 0.4 \text{ m}

. Find the electric field at the midpoint (

x = 0.2 \text{ m}

). Use

k = 9 \times 10^9

Example 3

easy

A test charge of

2 \text{ C}

feels a force of

10 \text{ N}

at a point. What is the electric field there?

Example 4

easy

A point charge

Q = 4 \text{ C}

. Find the field magnitude at

r = 2 \text{ m}

. Use

k = 9\times10^9

Example 5

easy

What are the units of electric field?

Example 6

easy

A field of

3 \text{ N/C}

acts on a charge of

5 \text{ C}

. Find the force.

A 5 C charge in a 3 N/C electric field; the force is F = qE

Example 7

easy

Which way does the electric field point near a positive point charge?

Example 8

easy

A point charge gives

E = 20 \text{ N/C}

r = 3 \text{ m}

. What is

E

r = 6 \text{ m}

Example 9

easy

Is electric field a vector or a scalar?

Example 10

easy

A charge

Q = 1 \text{ C}

at distance

r = 1 \text{ m}

. Find

E

. Use

k = 9\times10^9

Example 11

medium

Two charges,

+3 \text{ C}

x=0

and

+3 \text{ C}

x=4 \text{ m}

. What is the field magnitude at the midpoint

x=2 \text{ m}

Example 12

medium

Charge

+2 \text{ C}

at origin. Find the field at

r = 3 \text{ m}

. Use

k=9\times10^9

Example 13

medium

A uniform field of

500 \text{ N/C}

accelerates a

+2 \text{ C}

charge. Find the force.

A +2 C charge accelerated by a 500 N/C uniform field; the electric force is F

Example 14

medium

Charges

+4 \text{ C}

x=0

and

+4 \text{ C}

x=4 \text{ m}

. Find the field at

x=2 \text{ m}

Example 15

medium

A field does

E = kQ/r^2

. If

Q

triples and

r

doubles, by what factor does

E

change?

Example 16

medium

+5 \text{ C}

charge sits in a field; the force on it is

25 \text{ N}

east. What field acts on a

-5 \text{ C}

charge placed at the same point?

A −5 C charge in the same field that exerts 25 N east on a +5 C charge; by sign reversal the force is 25 N west.

Example 17

medium

At what distance from a

+9 \text{ C}

charge is the field

1 \text{ N/C}

? Use

k=9\times10^9

Example 18

medium

A field point is

r=5 \text{ m}

from

+1 \text{ C}

. A second

+1 \text{ C}

is added so the new field is along the same line and adds. The second charge gives the same magnitude. Total field?

Example 19

medium

A proton (

q=1.6\times10^{-19}

C) is in a field of

5\times10^5 \text{ N/C}

. Find the force on it.

A proton (q

Example 20

challenge

Charges

+q

(0,0)

and

+q

(0,a)

. Find the field magnitude at

(a,0)

in terms of

k,q,a

Example 21

challenge

An electron enters a uniform field

E=1000 \text{ N/C}

with the field along

+x

. It starts at rest. Find its acceleration magnitude. (

q=1.6\times10^{-19}

m=9.1\times10^{-31}

kg.)

An electron (negative charge) in a 1000 N/C field along +x feels a force in the −x direction, giving a ≈ 1.76×10¹⁴ m/s² acceleration.

Example 22

challenge

A dipole has

+q

(-a,0)

and

-q

(a,0)

. Find the field magnitude at the origin in terms of

k,q,a

, and its direction.

Both the +q charge (pushing right) and the −q charge (pulling right) contribute fields in the same +x direction at the origin; E_net

Example 23

easy

4\ \text{C}

charge feels a force of

20\ \text{N}

at a point. What is the electric field at that point?

Example 24

easy

A field of

200\ \text{N/C}

acts on a

-3\ \text{C}

charge. Find the force magnitude and direction relative to the field.

A −3 C charge in a 200 N/C field (pointing right); the force F

Example 25

easy

A point charge

Q = 2\times10^{-6}\ \text{C}

is at the origin. Find

E

r = 0.3\ \text{m}

. Use

k = 9\times10^9

Example 26

easy

A parallel-plate capacitor has plates

0.01\ \text{m}

apart with a

50\ \text{V}

potential difference. Find the field between the plates.

Between plates 0.01 m apart with 50 V across them, the uniform field E = V/d

Example 27

easy

If the distance from a point charge doubles, the field becomes ____ as strong.

Example 28

medium

Two equal positive charges

+q

sit at

(\pm a, 0)

. What is the direction of the net field at the origin?

Example 29

medium

On the line joining

+4\ \mu\text{C}

and

+1\ \mu\text{C}

separated by

3\ \text{m}

, find the location (measured from the

+4\ \mu\text{C}

) where the field is zero between them.

Example 30

medium

A uniform field

E = 2000\ \text{N/C}

points

+x

. A proton (

q = +1.6\times10^{-19}\ \text{C}

m = 1.67\times10^{-27}\ \text{kg}

) is released from rest in the field. Find its acceleration.

A proton at rest in a 2000 N/C field; F = qE

Example 31

medium

Find the field

E

at the surface of a sphere of radius

0.10\ \text{m}

carrying

1.0\ \mu\text{C}

of charge. Use

k = 9\times10^9

Example 32

medium

Two parallel plates separated by

5\ \text{mm}

have a uniform field

E = 8000\ \text{V/m}

. Find the potential difference.

Example 33

medium

+2\ \mu\text{C}

test charge feels a force of

6\ \text{mN}

at a point. What is the field there?

Example 34

medium

At what distance from a

+1\ \mu\text{C}

point charge is the field

9\times10^5\ \text{N/C}

? Use

k = 9\times10^9

Example 35

hard

Two charges

+3\ \mu\text{C}

(0,0)

and

-3\ \mu\text{C}

(0.6\ \text{m},0)

. Find the field at the midpoint

(0.3,0)

in magnitude and direction. Use

k = 9\times10^9

At the midpoint between +3 μC and −3 μC (0.3 m from each), both contributions point in +x; E_net

Example 36

hard

An oil drop of mass

3.2\times10^{-15}\ \text{kg}

carries charge

-3e

. What uniform vertical field

E

keeps it suspended? Use

g = 9.8\ \text{m/s}^2

Millikan-style equilibrium: the upward electric force on the negatively charged oil drop equals its weight mg

Example 37

hard

Charges

+q

(0,0)

and

+q

(a,0)

. Find the field at

(a/2, a/2)

in magnitude and direction.

Example 38

hard

Two infinite parallel plates carry equal-and-opposite surface charge density. If the field between them is

E_0

, what is the field just outside the plates (in the region not between them)?

Example 39

hard

A point charge

+Q

produces

E = 100\ \text{N/C}

r = 2\ \text{m}

. What is

E

r = 5\ \text{m}

Example 40

challenge

On the line joining

+9\ \mu\text{C}

x=0

and

-1\ \mu\text{C}

x=2\ \text{m}

, where does the net field vanish? (Search outside the segment.)

Example 41

challenge

Three charges

+q

sit at the vertices of an equilateral triangle of side

a

. Find the magnitude of the field at the centroid.

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Related Concepts

Electric Charge Force Coulomb's Law Electric Potential Magnetic Field

Background Knowledge

These ideas may be useful before you work through the harder examples.

electric chargeforce