Advanced Calculator
Enter each source charge as q, x, y, z, label. The z value is optional.
Formula Used
Coulomb force from source i:
Fᵢ = k q₀ qᵢ (r₀ − rᵢ) / |r₀ − rᵢ|³
Net force:
Fnet = Σ Fᵢ = (ΣFx) i + (ΣFy) j + (ΣFz) k
Magnitude:
|Fnet| = √(Fx² + Fy² + Fz²)
Electric field at target:
Enet = Fnet / q₀ = Σ k qᵢ (r₀ − rᵢ) / |r₀ − rᵢ|³
How To Use This Calculator
- Enter the target charge and its coordinate position.
- Select charge units and coordinate units.
- Enter each source charge on a separate line.
- Use negative values for negative charges.
- Choose vacuum, medium, or custom constant mode.
- Press the calculate button to see the vector result.
- Review the contribution table for each charge.
Understanding Net Electric Force
Net electric force comes from vector addition. Each source charge pushes or pulls the target charge. The final answer depends on charge signs. It also depends on distance and direction. A positive source repels a positive target. A negative source attracts a positive target. Mixed signs reverse the direction. The force size follows Coulomb's inverse square law. Direction needs coordinate geometry. That makes multi charge problems harder than single charge work.
Why Vector Components Help
A force is not only a number. It also has a direction. Component form separates the force into x, y, and z parts. This method prevents angle mistakes. It also works for two dimensional and three dimensional layouts. The calculator finds the displacement from each source charge to the target charge. It then divides that displacement by its distance. That gives the correct direction unit vector. The scalar force is then spread across each axis.
Charge Position Matters
Small position changes can cause large force changes. This happens because distance is squared in the denominator. Charges placed near the target can dominate the final result. Charges far away may still matter when their value is large. Balanced arrangements can produce zero force. Unbalanced arrangements create a clear resultant direction. Always enter coordinates using one position unit. Mixing centimeters and meters without conversion gives wrong answers. This page converts position units before solving.
Advanced Input Choices
The tool supports many charge units. You can enter coulombs, millicoulombs, microcoulombs, nanocoulombs, or picocoulombs. You can also choose the coordinate unit. The medium option adjusts the effective Coulomb constant. Vacuum uses the standard constant. Relative permittivity reduces force inside materials. A custom constant helps when a problem statement gives a special value. Precision control changes displayed digits without changing the internal calculation.
Reading The Result
The summary shows total force components first. It then shows the resultant magnitude. The x y plane angle uses the positive x axis as zero degrees. Positive angles rotate toward positive y. Direction angles compare the resultant with each coordinate axis. The electric field value divides net force by the target charge. This is useful when the target charge is a test charge. The contribution table shows every source charge separately. Use it to find the strongest interaction.
Good Practice Tips
Use signed charge values. Enter negative charges with a minus sign. Avoid placing a source charge at the target point. That makes distance zero. Coulomb's law cannot handle that case. Check your coordinate diagram before trusting numbers. Estimate the direction first. Then compare the estimate with the calculated vector. This habit catches sign errors early. It also improves problem solving confidence during exams. Review each component before accepting the final answer. When values look surprising, inspect the contribution table carefully. One misplaced sign can rotate the whole resultant. Recheck units after changing any example line before final submission again.
Example Data
| Source charge | x | y | z | Meaning |
|---|---|---|---|---|
| 4 uC | 0.25 m | 0 m | 0 m | Positive source right of target |
| -3 uC | 0 m | 0.40 m | 0 m | Negative source above target |
| 1.5 uC | -0.35 m | -0.15 m | 0 m | Positive lower left source |
FAQs
What does net electric force mean?
It is the vector sum of all electric forces acting on a target charge. The final force includes both magnitude and direction.
Can I use negative charge values?
Yes. Enter a minus sign before any negative charge. The calculator uses the sign to decide attraction or repulsion.
Does charge order change the answer?
No. Vector addition is independent of order. Each source contribution is calculated separately, then added component by component.
Why is distance cubed in the vector formula?
The scalar law uses distance squared. The extra distance appears when the displacement vector is normalized into a direction vector.
Can this solve three dimensional problems?
Yes. Enter z coordinates for the target and each source. Leave z as zero for two dimensional layouts.
What happens in a material medium?
The effective force is reduced by relative permittivity. Choose that mode and enter the material value given in your problem.
Why did I get a zero distance error?
A source charge was placed exactly at the target point. Coulomb's law becomes undefined when separation is zero.
What is the xy direction angle?
It is the angle of the net force projection in the x y plane. Zero degrees points along positive x.
How is electric field related to force?
Electric field equals force per unit target charge. It shows the field created by source charges at the target location.
Can forces cancel each other?
Yes. Equal opposite vector components can cancel. The magnitude may become zero in symmetric charge arrangements.
Which unit should I use for coordinates?
Use the unit that matches your diagram. The calculator converts selected coordinate units into meters before solving.