Units of Coulomb's Constant

[ZedCar]

Coulomb's constant, which appears in Coulomb's Law, contains ε0.

The units of ε0 being F/m

Are the units of Coulomb's constant therefore F/m ?

Thank you.

 

[PeterO]

Coulomb's constant, which appears in Coulomb's Law, contains ε0.

The units of ε0 being F/m

Are the units of Coulomb's constant therefore F/m ?

Thank you.

I would have thought F^-1m since k_e = 1/(4∏ε_o)

 

[ehild]

Coulomb's constant, which appears in Coulomb's Law, contains ε0.

The units of ε0 being F/m

Are the units of Coulomb's constant therefore F/m ?

Thank you.

Yes, but farad can be derived from the basic units of the SI system, so the unit of ε0 is A²s⁴kg^-1m^-3 in terms of the basic SI units.

ehild

 

[ehild]

I would have thought F^-1m since k_e = 1/(4∏ε_o)

For parallel plate capacitors, C=εA/d (A is the surface of the plates, d is the distance between them) so farad=[ε]m.

ehild

 

[asteriatic]

Yes, the units of Coulomb's constant are indeed F/m. This is because Coulomb's constant, also known as the electric constant, is a proportionality constant that relates the strength of the electric force between two point charges to the distance between them. The electric force is measured in Newtons (N) and the distance is measured in meters (m), so the units of Coulomb's constant must be in Nm^2/C^2. By substituting the units of the electric constant, ε0, which is measured in Farads per meter (F/m), we get the final unit of F/m for Coulomb's constant. This unit represents the force per unit charge that is exerted between two point charges at a certain distance.