Question

A hydrogen atom in the normal state is locatred at a distance `r=2. 5cm` from a long straigh condctor carrying a current `I= 10A`. Find the force acting on the atom.

Answer 1

The magnetic field at a distacne `r` from a long current carrying wire is mostly tangential and given by
`B_(varphi)=(mu_(0)I)/(2 pi r)=(mu_(0))/(4pi)(2I)/(r )`
The force on a magnetic dipole of mement `vec(mu)` due to this magnetic iels is also tangential and has magnitude `(vec(mu).grad)B_(varphi)`
This force is nonvanishing only when the component of `vec(mu)` along `vec(r )` non zero. Then
`F=mu_(r )(del)/(del r)B_(varphi)= -mu_(r )(mu_(0))/(4pi)(2I)/(r^(2))`
Now the maximum value of `mu_(r )=+-mu_(B)` Thus the force is
`F_(max)=mu_(B)(mu_(0))/(4pi)(2I)/(r^(2))= 2.97xx10^(-26)N`