1. What is the Dimensional Formula of Electric Force?

Definition: The dimensional formula of electric force is [M L T⁻²], which represents the fundamental dimensions of mass, length, and time in the International System of Units (SI).

Purpose: This formula helps physicists and engineers analyze electric force in terms of its fundamental dimensions, enabling unit conversions and dimensional analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( M \) — Mass (kilograms)
• \( L \) — Length (meters)
• \( T \) — Time (seconds)

Explanation: The formula shows how electric force depends on mass, length, and time dimensions, which are the fundamental quantities in physics.

3. Importance of Dimensional Analysis

Details: Dimensional analysis helps verify equations, convert between units, and understand the fundamental nature of physical quantities like electric force.

4. Using the Calculator

Tips: Enter values for mass (kg), length (m), and time (s). The calculator will compute the dimensional value of electric force in [M L T⁻²] units.

5. Frequently Asked Questions (FAQ)

Q1: Why is the time dimension squared in the denominator?
A: This comes from Newton's second law (F=ma) where acceleration (a) has dimensions [L T⁻²], making force [M L T⁻²].

Q2: How does this relate to Coulomb's Law?
A: Coulomb's Law (F=kq₁q₂/r²) also results in [M L T⁻²] dimensions when analyzed dimensionally.

Q3: What are the SI units for electric force?
A: The SI unit is the newton (N), which equals 1 kg·m/s², matching the [M L T⁻²] dimensions.

Q4: Can I use this for other types of forces?
A: Yes, all forces (gravitational, magnetic, etc.) share the same dimensional formula [M L T⁻²].

Q5: How is this different from units?
A: Dimensions represent the physical nature (mass, length, time), while units are specific measurements (kg, m, s) of those dimensions.