Prove that the equation is homogeneous where U is permittivity, I1 and I2 is current,a is distance

The equation provided is $F = \frac{\mu_0 I_1 I_2}{2a}$.
To prove that an equation is homogeneous, we must show that the dimensions of the Left Hand Side (LHS) are equal to the dimensions of the Right Hand Side (RHS).

First, let's clarify the terms:

• The symbol $\mu_0$ represents the permeability of free space, not permittivity (which is typically denoted by $\epsilon_0$). We will use the dimension for permeability.
• The expression $\frac{\mu_0 I_1 I_2}{2a}$ is dimensionally consistent with force per unit length between two parallel current-carrying wires,