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Electric Field Calculator

Calculate electric field strength, electric potential, and electric force with interactive visualization

Parameters

Cⓘ
Enter the source charge (positive or negative)
mⓘ
Distance from the source charge
Cⓘ
Test charge to calculate force on
Electric Field Analysis
Enter values to calculate electric field, potential, and force

Calculated Values

Electric Field:
899000.00;N/C899000.00;N/C
Electric Potential:
89900.00;V89900.00;V
Electric Force:
0.00;N0.00;N
Potential Energy:
0.00;J0.00;J

Examples

Example 1: Point Charge Field

A 1μC charge at 10cm distance.

  • Electric Field: 899000899000
  • Electric Potential: 8990089900
  • Electric Force: 0.0008990.000899

Example 2: Electron Field

An electron (-1.6×10⁻¹⁹C) at 1nm distance.

  • Electric Field: 143840143840
  • Electric Potential: −1.4384-1.4384
  • Electric Force: 1.44e−141.44e-14

Example 3: Large Charge

A 1mC charge at 1m distance.

  • Electric Field: 89900008990000
  • Electric Potential: 89900008990000
  • Electric Force: 8.998.99

Electric Fields and Forces

An electric field is a region of space around a charged particle where other charged particles experience an electric force. The electric field strength at any point is defined as the force per unit charge that would be experienced by a positive test charge placed at that point.

The electric field strength due to a point charge is given by E = k|q|/r², where k is Coulomb's constant (8.99 × 10⁹ N⋅m²/C²), q is the source charge, and r is the distance from the charge. The field points away from positive charges and toward negative charges.

Electric potential is the electric potential energy per unit charge at a point in an electric field. For a point charge, the potential is V = kq/r. Unlike electric field, potential is a scalar quantity and can be positive or negative depending on the sign of the charge.

The electric force on a test charge in an electric field is given by F = qE, where q is the test charge and E is the electric field strength. This force is attractive if the charges have opposite signs and repulsive if they have the same sign.

Electric field lines are imaginary lines that show the direction of the electric field at each point. They start on positive charges and end on negative charges, never crossing each other. The density of field lines indicates the strength of the field.

Key Concepts

  • Electric Field: E = k|q|/r² (force per unit charge)
  • Electric Potential: V = kq/r (energy per unit charge)
  • Electric Force: F = qE (force on test charge)
  • Coulomb's Constant: k = 8.99 × 10⁹ N⋅m²/C²
  • Field Direction: Away from positive, toward negative
  • Field Lines: Show direction and strength of field

Real-World Applications

  • Capacitors: Understanding electric fields between plates
  • Particle Accelerators: Controlling charged particle motion
  • Electrostatic Precipitators: Removing particles from air
  • Cathode Ray Tubes: Deflecting electron beams
  • Lightning Protection: Understanding electric field buildup

Physics Equations

Electric Field Strength:
E=k∣q∣r2E = k\frac{|q|}{r^2}
Electric Potential:
V=kqrV = k\frac{q}{r}
Electric Force:
F=qEF = qE
Coulomb's Law:
F=kq1q2r2F = k\frac{q_1 q_2}{r^2}
Potential Energy:
U=qVU = qV

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Identify Known Values

List the given values from the problem:

Equation:

\text{Given: } q = ${q} \text{ C}, r = ${r} \text{ m}, q_{test} = ${qTest} \text{ C}

Calculation:

q=0.000001 Cr=0.1 mqtest=1e−9 Cq = 0.000001 \text{ C} \\ r = 0.1 \text{ m} \\ q_{test} = 1e-9 \text{ C}

Explanation:

We start by identifying what values we know and what we need to find.

2

Step 2: Calculate Electric Field

Use the electric field formula:

Equation:

E=k∣q∣r2E = k\frac{|q|}{r^2}

Calculation:

E=8990000000×∣0.000001∣0.12=899000.00 N/CE = 8990000000 \times \frac{|0.000001|}{0.1^2} = 899000.00 \text{ N/C}

Explanation:

Electric field strength is calculated using Coulomb's law divided by distance squared.

3

Step 3: Calculate Electric Potential

Use the electric potential formula:

Equation:

V=kqrV = k\frac{q}{r}

Calculation:

V=8990000000×0.0000010.1=89900.00 VV = 8990000000 \times \frac{0.000001}{0.1} = 89900.00 \text{ V}

Explanation:

Electric potential is the electric potential energy per unit charge.

4

Step 4: Calculate Electric Force

Use the electric force formula:

Equation:

F=qtestEF = q_{test}E

Calculation:

F=1e−9×899000.00=0.000899 NF = 1e-9 \times 899000.00 = 0.000899 \text{ N}

Explanation:

Electric force on a test charge is the product of the test charge and electric field strength.

Frequently Asked Questions (FAQ)

What is an electric field?

An electric field is a region of space around a charged particle where other charged particles experience an electric force. It represents the force per unit charge.

How do I calculate electric field strength?

Electric field strength is calculated using E = k|q|/r², where k is Coulomb's constant, q is the source charge, and r is the distance from the charge.

What is the difference between electric field and electric potential?

Electric field is a vector quantity representing force per unit charge, while electric potential is a scalar quantity representing energy per unit charge. Field is related to force, potential is related to energy.

How does the sign of charge affect the electric field?

The magnitude of the electric field depends only on the absolute value of the charge. The direction points away from positive charges and toward negative charges.

What happens to electric field strength with distance?

Electric field strength decreases with the square of the distance (1/r²). Doubling the distance reduces the field strength to one-fourth.

How do I calculate electric force?

Electric force on a test charge is calculated using F = qE, where q is the test charge and E is the electric field strength at that point.

Practice MCQs

  1. If the distance from a charge is doubled, the electric field strength becomes:
  2. What is the electric field strength 1m from a 1μC charge?
  3. The electric field points:
  4. If a test charge is negative, the electric force is:
  5. Electric potential is: