Dimensional formula of Electric potential energy

How to get the dimensional formula of electric potential energy

1. Start from the definition: electric potential energy = electric charge × electric potential.
2. electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
3. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
4. energy = mass × velocity², so energy is [M] × [L T^-1]² = [M L² T^-2].
5. electric potential = energy / electric charge, so electric potential is [M L² T^-2] / [T A] = [M L² T^-3 A^-1].
6. Put in the dimension of each part: [T A] × [M L² T^-3 A^-1].
7. Add the powers of each base quantity: [M L² T^-2].

Quantities with the dimensions [M L² T⁻²]

• Work
• Energy
• Kinetic energy
• Potential energy
• Torque
• Torsional constant
• Gravitational potential energy
• Strain energy
• Heat
• Internal energy
• Work function
• Photon energy
• Binding energy

Equal dimensions do not make them the same quantity. Compare electric potential energy with the others in the full grid.

Three questions on electric potential energy

Related quantities

• q Electric charge [T A]
• E Electric field [M L T⁻³ A⁻¹]
• V Electric potential [M L² T⁻³ A⁻¹]
• V Potential difference [M L² T⁻³ A⁻¹]
• ε Electromotive force (emf) [M L² T⁻³ A⁻¹]
• Φ_E Electric flux [M L³ T⁻³ A⁻¹]