What are the units for magnetic pressure?

In summary, magnetic pressure is the force exerted by a magnetic field on a material, similar to the pressure of a gas or liquid. It is measured in units of pascals (Pa) or newtons per square meter (N/m²) and can be calculated by multiplying the square of the magnetic field strength by the permeability of the material. Magnetic pressure differs from magnetic field strength in that it is a result of the interaction between the field and charged particles, while field strength is a property of the field itself. Real-world applications of magnetic pressure include technological devices such as MRI machines and plasma physics experiments, as well as its role in the dynamics of cosmic bodies.
  • #1
terryphi
59
0
The formula for magnetic pressure is

P[itex]_{B}[/itex] = [itex]\frac{B^{2}}{2\mu_{0}}[/itex]

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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  • #2
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}]##
 

1. What is magnetic pressure?

Magnetic pressure is the force exerted by a magnetic field on a material. It is similar to the pressure exerted by a gas or liquid, but in this case, it is caused by the interaction between magnetic fields and charged particles.

2. What units are used to measure magnetic pressure?

Magnetic pressure is typically measured in units of pascals (Pa) or newtons per square meter (N/m²). Other common units include dynes per square centimeter (dyn/cm²) and pounds per square inch (psi).

3. How is magnetic pressure calculated?

Magnetic pressure can be calculated by multiplying the square of the magnetic field strength by the permeability of the material. It can also be derived from the Lorentz force equation, which takes into account the velocity of the charged particles.

4. What is the difference between magnetic pressure and magnetic field strength?

Magnetic pressure is a measure of the force exerted by a magnetic field, while magnetic field strength is a measure of the intensity of the field itself. In other words, magnetic pressure is the result of the interaction between a magnetic field and charged particles, while magnetic field strength is a property of the field itself.

5. What are some real-world applications of magnetic pressure?

Magnetic pressure is a crucial component in many technological devices, such as MRI machines, particle accelerators, and magnetic levitation trains. It also plays a significant role in the dynamics of cosmic bodies, such as stars and planets, as well as in plasma physics experiments.

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