Answer
(a) $1.6\times 10^{11}N$
(b) The force from the magnetar is 280,000 times greater than the electron-proton force within a hydrogen atom.
Work Step by Step
(a) We know that
$F=BILsin\theta$
We plug in the known values to obtain:
$F=(6.5\times 10^{10}T)(1.1A)(2.5m)sin65^{\circ}$
$F=1.6\times 10^{11}N$
(b) We know that
$F_e=Bevsin\theta$
$F_e=(6.5\times 10^{10}T)(1.602\times 10^{-19}C)(2.2\times 10^6m/s)sin90^{\circ}$
$F_e=23\times 10^{-3}=23mN$
and the force exerted on an electron in a hydrogen atom is given as
$F_H=\frac{1}{4\pi \epsilon_{circ}}\frac{e^2}{r_H^2}$
$\implies F_H=(9\times 10^9)\times \frac{(1.602\times 10^{-19})^2}{(5.2\times 10^{-11}m)^2}$
$F_H=8.2\times 10^{-8}$
Thus, the force from the magnetar is 280,000 times greater than the electron-proton force within a hydrogen atom.
