Show that the quantity B2/(2Ho) has the units of energy density.

Sure, let's break it down:

1. B is the magnetic field, which is measured in Tesla (T). So, B^2 would be in T^2.

2. Ho is the permeability of free space, which is measured in Henry per meter (H/m).

3. Therefore, B^2/Ho would be in T^2/(H/m).

4. Now, 1 Henry (H) is equivalent to kg⋅m^2⋅s^-2⋅A^-2 (kilogram meter squared per second squared per ampere squared).

5. So, B^2/Ho would be in T^2/(kg⋅m^2⋅s^-2⋅A^-2/m) = T^2⋅m/(kg⋅m^2⋅s^-2⋅A^-2).

6. But 1 Tesla (T) is equivalent to kg⋅s^-2⋅A^-1 (kilogram per second squared per ampere).

7. Therefore, B^2/Ho would be in (kg⋅s^-2⋅A^-1)^2⋅m/(kg⋅m^2⋅s^-2⋅A^-2) = kg⋅m⋅s^-2 = Joules per meter cubed (J/m^3).

8. Joules per meter cubed (J/m^3) is the unit of energy density.

Therefore, the quantity B^2/(2Ho) has the units of energy density.