所選文字: Show that the quantity B^2/(2μ0) has the units of energy density. 回答問題

Sure, let's break this down:

1. B is the magnetic field, which is measured in Tesla (T).

2. μ0 is the permeability of free space, which is measured in henries per meter (H/m).

3. The square of the magnetic field B^2 would therefore have units of Tesla squared (T^2).

4. Dividing B^2 by μ0 gives us units of (T^2) / (H/m).

5. Now, we need to express this in terms of energy density. Energy density is the amount of energy stored in a given system or region of space per unit volume, and it is measured in joules per cubic meter (J/m^3).

6. We know that 1 H = 1 J/(A^2), where A is amperes, and 1 T = 1 (kg/(s^2A)).

7. Substituting these units in, we get (T^2) / (H/m) = ((kg/(s^2A))^2) / (J/(A^2)m) = (kg^2/(s^4A^2)) / (J/(A^2)m).

8. Simplifying this, we get kg^2/(s^4A^2) * (A^2m/J) = kg^2/(s^4) * m/J = kg/(s^2) * m^2/s = kg*m/s^3 = J/m^3.

So, the quantity B^2/(2μ0) indeed has the units of energy density.