Calculate electric field strength from point charges using Coulomb's law. Compute force on charges, determine charge from field, and find net field from two charges with step-by-step physics solutions.
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Coulomb's Constant (k):k = 8.99 × 10⁹ N·m²/C²
Electric Field (E)
0
N/C
Force (F = qE)
—
Newtons (N)
Mode
Point Charge
Calculation method used
📝 Step-by-Step Solution
Real-World Electric Field Examples
⚡ Electric Field of a Single Proton
Problem: A proton has a charge of +1.602 × 10⁻¹⁹ C. What is the electric field at a distance of 0.053 nm (approximate Bohr radius)?
This enormous field is what binds electrons to the nucleus in atoms. The field points radially outward from the proton.
🔋 Force on an Electron in a Uniform Field
Problem: An electron (q = -1.602 × 10⁻¹⁹ C) is placed in a uniform electric field of 500 N/C. What force does it experience?
Solution: Using F = qE
F = (-1.602 × 10⁻¹⁹)(500) = -8.01 × 10⁻¹⁷ N
The negative sign indicates the force is opposite to the field direction. This is how charged particles are manipulated in devices like cathode ray tubes and particle accelerators.
📥 Finding Charge from Electric Field
Problem: At a distance of 0.5 m from a point charge, the electric field is measured to be 360 N/C. What is the charge?
This configuration is called an electric dipole. The field at the midpoint is the sum of both contributions since they point in the same direction.
Electric Field Formula & Guide
E = kQ / r²
Electric field from a point charge (Coulomb's Law)
Where E is electric field (N/C), k = 8.99 × 10⁹ N·m²/C² is Coulomb's constant, Q is the charge (C), and r is the distance from the charge (m).
F = qE
Force on a charge in an electric field
Where F is the electrostatic force (N), q is the test charge (C), and E is the electric field (N/C). A positive charge experiences force in the same direction as the field; a negative charge experiences force opposite to the field.
E_net = E₁ + E₂ + ...
Principle of superposition for electric fields
The net electric field from multiple charges is the vector sum of the individual fields. For the two-point charge calculation at the midpoint: each field is calculated using E = kQ/(d/2)², and the direction depends on the sign of the charge (away from positive, toward negative).
Key Concepts
📌 What is an Electric Field?
An electric field is a region around a charged particle where a force would be exerted on other charged particles. It is a vector field — it has both magnitude and direction. The SI unit is Newtons per Coulomb (N/C) or Volts per meter (V/m).
📌 Direction of Electric Field
The electric field points away from positive charges and toward negative charges. A positive test charge placed in the field will experience a force in the direction of the field.
📌 Coulomb's Constant (k)
Coulomb's constant k = 8.99 × 10⁹ N·m²/C² relates the force between two charges to their magnitudes and distance. It appears in both Coulomb's law (F = kQ₁Q₂/r²) and the electric field equation (E = kQ/r²).
📌 Superposition Principle
The total electric field at any point from multiple charges is the vector sum of the fields from each individual charge. This principle allows us to calculate net fields from complex charge distributions by adding contributions from each point charge.
⚡
Point Charge Field
Calculate electric field strength from a single point charge using E = kQ/r². Supports Coulombs, microcoulombs, and nanocoulombs with meter, cm, and mm distance units.
🔋
Force on Charge
Compute the electrostatic force on a charge placed in an electric field using F = qE. Supports N, mN, and μN force units.
📥
Charge from Field
Determine the charge that produces a given electric field at a known distance. Perfect for experimental physics and lab work.
🔄
Two-Point Charge Field
Calculate the net electric field at the midpoint between two point charges using the superposition principle.
⚠️ Important Note: This calculator assumes point charges in a vacuum. Real-world electric fields may be affected by the presence of other charges, conductors, and dielectric materials. The formulas assume the distance r is much larger than the physical size of the charged object. For accurate results in complex scenarios, consider using more advanced electromagnetic simulation tools.
Frequently Asked Questions
What is an electric field in physics?
An electric field is a physical field that surrounds electric charges and exerts force on other charges placed within it. It is defined as the force per unit positive test charge: E = F/q. The electric field is a vector quantity, meaning it has both magnitude and direction. The SI unit is Newtons per Coulomb (N/C) or equivalently Volts per meter (V/m).
How do you calculate electric field from a point charge?
The electric field from a point charge is calculated using E = kQ/r², where k = 8.99 × 10⁹ N·m²/C² is Coulomb's constant, Q is the charge, and r is the distance from the charge. The field points away from positive charges and toward negative charges. For example, a 1 μC charge at 0.1 m produces an electric field of E = (8.99×10⁹)(1×10⁻⁶)/(0.1)² = 8.99×10⁵ N/C.
What is the relationship between electric field and force?
The relationship is F = qE, where F is the force on a charge, q is the charge magnitude, and E is the electric field. A positive charge experiences a force in the same direction as the electric field, while a negative charge experiences a force in the opposite direction. This is the fundamental principle behind how electric fields interact with charged particles in devices like cathode ray tubes, particle accelerators, and electrostatic precipitators.
What is the difference between electric field and electric potential?
Electric field (E) is a vector quantity that describes the force per unit charge at a point in space. Electric potential (V) is a scalar quantity that describes the potential energy per unit charge. The electric field is related to the negative gradient of the potential: E = -dV/dr. While the electric field tells you the direction and magnitude of the force on a charge, the potential tells you how much work is needed to move a charge to that position.
What happens to the electric field when distance changes?
The electric field follows an inverse square law: E ∝ 1/r². This means if you double the distance from a charge, the electric field decreases to one-fourth its original value. If you triple the distance, it decreases to one-ninth. Conversely, if you halve the distance, the electric field quadruples. This rapid decrease with distance is why electric fields are only significant close to their source charges.
How is Coulomb's law related to the electric field?
Coulomb's law describes the force between two charges: F = kQ₁Q₂/r². The electric field equation E = kQ/r² is derived from Coulomb's law by considering the force on a unit positive test charge. Specifically, if Q₂ is a test charge q, then F = kQq/r², and dividing by q gives E = F/q = kQ/r². Coulomb's constant k is the same in both equations.