In a proton accelerator used in elementary particle physics experiments, the trajectories of protons are controlled...
What is the magnetic-field energy in a 11.0 cm^3 volume of space where = 2.80 T?
Homework Answers
The concepts used to solve this problem are energy density in magnetic field and magnetic field energy.
Initially, use the relationship between magnetic field, energy density and permeability to find the energy density in magnetic field.
Finally, use the relationship between volumes of space, energy density in magnetic field to find the magnetic field energy.
The amount of energy saved in a system per unit volume is explained as energy density.
The expression energy density in magnetic field is given below:
Here, magnetic field is 
, energy density in magnetic field is 
, and permeability is 
.
The expression for magnetic field energy of a given volume of space is given below:
Here, magnetic field energy is 
, and volume is 
.
The expression energy density in magnetic field is given below:
Substitute 
for 
and 
for 
.
The expression for magnetic field energy of a given volume of space is given below:
Substitute 
for 
and 
for 
.
Thus, the magnetic field energy of a given volume of space is 
.
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