Question

A current I flows in a long thin walled cylinder of radius R. What pressure do the walls of the cylinder experience?

• A. $\frac{{\mu }_{0}I}{8\pi R}$
  
• B. $\frac{{\mu }_0{I}^2}{8{\pi }^2{R}^2}$
  
• C. $\frac{{\mu }_0{I}^2}{16\pi R^2}$
  
• D. $\frac{{\mu }_{0}I}{4{\pi }^{2}R}$
  

Answer 1

The correct option is B

$\frac{{\mu }_0{I}^2}{8{\pi }^2{R}^2}$

The magnetic field outiside the cylinder is $\frac{{\mu }_{0}I}{2\times 2\pi R}$
The magnetic fied inside the cylinder is $0$
The magnetic field in the inside the conductor is the average of the above two $=\frac{{\mu }_{0}I}{4\times 2\pi R}$
The current through a small strip of width $dl$ is given by $\frac{Idl}{2\pi r}$
Hence, the force acting on it given by $F=BiL=\frac{{\mu }_{0}I}{4\times 2\pi R}\frac{Idl}{2\pi r}L$
The area of the strip is given by $A=Ldl$
Hence the pressure on the strip is given by $\frac{F}{A}=\frac{{\mu }_0{I}^2}{8{\pi }^2{R}^2}$