Electric Field Of A Point Charge Calculator - Field Strength & Direction

An electric field of a point charge calculator finds the electric field E produced by a single point charge q at any distance r, using the relation E = k q / r^2 with the Coulomb constant k = 8.9875517923e9 N m^2/C^2. It reports the field magnitude in newtons per coulomb (which equals volts per meter) and, because the field is a vector, the radial direction it points.

• • Introductory electrostatics homework: Compute the field of a 1 nC charge sitting 10 cm away instead of doing the arithmetic by hand for every part of a problem set.
• • Force on a sensor or test charge: Drop a known test charge into the field input to read the force F = q_test E it would feel at that point, which is how field is defined experimentally.
• • Checking field direction for sign of charge: Confirm whether the field points outward (positive source charge) or inward (negative source charge) before sketching field lines.
• • Comparing a single charge to a system: Get the baseline field of one charge before adding contributions from others by superposition in a multi-charge layout.

Field is defined as force per unit charge, so once you know E you also know the push any other charge would feel there. That makes the point-charge field the building block for every more complicated electrostatics problem.

The field of one charge is exactly what produces the Coulomb force on a second charge, so the coulombs-law-calculator solves F = k q1 q2 / r^2 from the same two inputs of charge and distance.

The calculator plugs the source charge q and the distance r into the point-charge field law E = k |q| / r^2, then sets the direction from the sign of q and multiplies by an optional test charge to give the force.

• q: Source point charge in coulombs. The absolute value sets the magnitude; the sign sets the direction.
• r: Distance from the charge to the field point in meters. The denominator is r squared.
• k: Coulomb constant, 1/(4 pi epsilon_0), about 8.9876e9 N m^2/C^2.
• q_test: Optional charge placed at distance r. The force it feels is F = q_test E.

Because the field is a vector, the magnitude tells you how strong it is and the sign of q tells you which way it points. Negative-charge examples simply flip the direction reported by the tool.

According to Wikipedia - Electric field, the electric field of a point charge at distance r has magnitude E = (1/(4 pi epsilon_0)) |q| / r^2, directed radially outward from a positive charge and inward toward a negative charge.

For the same point charge the field is the negative gradient of the electric potential, so the electric-potential-calculator returns V = kq/r and shows directly why E grows as 1/r^2 while V falls only as 1/r.

An electric field of a point charge calculator relies on four ideas to explain why the field falls off as 1/r^2, why the direction depends on the sign of the charge, and how force on a second charge follows from the field.

These four ideas carry over to every superposition problem: each charge contributes its own kq/r^2 field, and the total field is the vector sum of the radial contributions.

The electric part of the lorentz-force is exactly F = q E from this field, so the same E you compute here drives the straight-line push on a stationary charge in that tool.

Four steps take you from a charge and a distance to a field magnitude, direction, and the force on a test charge.

1. 1 Enter the source charge q: Type the point charge in coulombs. Try 1e-9 for 1 nC, or 1.602176634e-19 for a single proton charge. Use a negative value for an electron or any negative charge.
2. 2 Enter the distance r: Type the distance from the charge to the point of interest in meters. Use any positive value; the calculator guards against r = 0.
3. 3 Optionally enter a test charge: Type a test charge in coulombs if you want the force it feels. Leave it at 0 to report only the field.
4. 4 Read the field and force: The result panel shows E in N/C, the radial direction, and the force on the test charge in newtons.

For a 1 nC charge 0.1 m away with no test charge, set q = 1e-9, r = 0.1, q_test = 0. The page returns E = 898.755 N/C, direction outward, matching the hand calculation kq/r^2.

When several charges sit near each other and screening changes the net pull, the effective-charge-calculator returns the effective charge that replaces the cluster for the same field at a distance.

An electric field of a point charge calculator gives you five reasons to compute the point-charge field with this page instead of by hand.

• • Exact Coulomb constant: The tool uses k = 8.9875517923e9, the CODATA value, so results match textbook and exam answers without rounding the constant early.
• • Magnitude and direction together: Both the field strength and the outward or inward direction appear in one panel, so the vector nature of the field is never lost.
• • Force on a test charge in one step: Entering a test charge returns F = q_test E immediately, which is the quantity labs and problems actually ask for.
• • Sign-aware for positive and negative charges: Negative source charges flip the reported direction automatically, removing a common sign-error trap.
• • Edge-case safe: A zero charge gives a zero field and r = 0 returns a guarded 'undefined' instead of a divide-by-zero crash, so the page stays usable on textbook edge cases.

Because the point-charge field is the foundation of superposition, getting one charge exactly right makes every multi-charge field problem that builds on it easier to check.

After you have the electric force q_test E, the net-force-calculator adds it to gravity, tension, or other forces to give the net push on a charged object.

Four things that change the field, plus two caveats about when the single point-charge model stops being accurate.

• • The formula describes an ideal point charge in empty space. Near a conductor or dielectric the surrounding material changes the local field, so the vacuum result is an approximation.
• • At very small distances the point-charge model breaks down because real charges are not mathematical points and quantum effects appear; treat results at atomic scales as estimates.

For most introductory physics and lab work the single point-charge field in vacuum is the right starting point, and the four factors above are everything that changes the answer.

According to OpenStax - University Physics Volume 2, the electric field of a point charge is the force per unit charge E = F/q_test, so a test charge placed in the field feels a force F = q_test E.

According to NIST - CODATA Constants, the Coulomb constant k = 1/(4 pi epsilon_0) has the CODATA recommended value 8.9875517923e9 N m^2/C^2.

The field is the gradient of the electric potential energy, so the potential-energy-calculator returns U = qV for the same charge and distance you entered here.