Magnitude Of Electric Force Calculator With Time

Electric Force Formula With Time:

\[ F = k \cdot \frac{q_1 \cdot q_2}{(r + v \cdot t)^2} \]

Coulomb's Constant (k):

N·m²/C²

Charge 1 (q₁):

Charge 2 (q₂):

Initial Distance (r):

Relative Velocity (v):

m/s

Time (t):

Electric Force (F):

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1. What is the Electric Force Equation With Time?

The electric force equation with time extends Coulomb's law to account for changing distance between charges due to relative motion. It calculates the magnitude of electrostatic force between two point charges as their separation changes over time.

2. How Does the Calculator Work?

The calculator uses the modified Coulomb's law formula:

\[ F = k \cdot \frac{q_1 \cdot q_2}{(r + v \cdot t)^2} \]

Where:

\( F \) — Electric force magnitude (N)
\( k \) — Coulomb's constant (8.99 × 10⁹ N·m²/C²)
\( q_1, q_2 \) — Electric charges (C)
\( r \) — Initial separation distance (m)
\( v \) — Relative velocity between charges (m/s)
\( t \) — Time elapsed (s)

Explanation: The equation accounts for the changing distance between charges due to their relative motion over time, affecting the electrostatic force between them.

3. Importance of Electric Force Calculation

Details: Calculating time-dependent electric forces is crucial for understanding dynamic electromagnetic systems, charged particle motion, and time-varying electrostatic interactions in physics and engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure initial distance and time are non-negative. The relative velocity can be positive (increasing distance) or negative (decreasing distance).

5. Frequently Asked Questions (FAQ)

Q1: What happens when the distance becomes zero?
A: The force becomes undefined (infinite) as the denominator approaches zero, which reflects the theoretical singularity in Coulomb's law at zero separation.

Q2: Can this be used for moving charges in magnetic fields?
A: This calculator only considers electrostatic forces. For complete electromagnetic analysis including magnetic effects, additional equations are needed.

Q3: How does relative velocity affect the force?
A: Positive velocity decreases force over time by increasing distance, while negative velocity increases force by decreasing distance between charges.

Q4: Is air resistance considered in this calculation?
A: No, this is a pure electrostatic calculation that assumes vacuum conditions and neglects any medium effects or drag forces.

Q5: What are typical values for the parameters?
A: Charges are typically in microcoulombs (μC), distances in meters, velocities in m/s, and forces in newtons. Coulomb's constant is approximately 8.99 × 10⁹ N·m²/C².