What are the units for magnetic pressure?

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SUMMARY

The units for magnetic pressure are derived from the formula P_{B} = B^{2}/(2μ_{0}), where P_{B} represents magnetic pressure in Pascals. The right-hand side of the equation consists of units T² H⁻¹ m, which can be simplified through dimensional analysis to match the left-hand side. The discussion emphasizes the importance of understanding the relationships between force, area, and magnetic field strength in this context.

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  • Familiarity with magnetic field concepts, including magnetic flux density (B).
  • Knowledge of dimensional analysis techniques.
  • Basic understanding of the permeability of free space (μ₀) and its units.
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terryphi
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The formula for magnetic pressure is

P_{B} = \frac{B^{2}}{2\mu_{0}}

Now, the units on the left hand side are clearly Pascals, but the units on the RHS are T^2 H^-1 m.

I've been trying and I can't see how to make the units on the RHS equal the units on the LHS. does anyone have any insight?
 
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Use dimensional analysis.
I'll start you off:

##[P]=[F][A]^{-1}## since P=F/A
##=[F][qv]^{-1}## since F=qvB.

##[\mu_0]=[m^2 kg C^{-2}]##
 

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