PLZ ANYONE ANSWER THIS QUESTION IN DETAIL..
AN ELECTRON & A PROTON WITH EQUAL MOMENTUM ENTER PREPENDICULARLY INTO UNIFORM MAGNETIC FIELD. THEN WHICH OF FOLLOWING IS TRUE -:
A) THE PATH OF PROTON SHALL BE MORE CURVED THAN THAT OF ELECTRON.
B) THE PATH OF PROTON SHALL BE LESS CURVED THAN THAT OF ELECTRON.
C) BOTH ARE EQUALLY CURVED.
D) NONE OF THESE .
The force that curves the trajectory of a charged particle `q` in a magnetic field of intensity `B` is the Lorentz force:
`|F|=|q*(v xx B)| =qvB`
if vector speed `v` is perpendicular to vector induction `B` .
The radius of the curvature of the trajectory comes from the condition that the Lorentz force is equal to the centrifugal force.
`q*v*B =m*v^2/R rArr R = (m/q)*(v/B) = (m*v)/q *B`
Since in the problem, the linear momentum is the same for both electron and proton, apart from the fact that their path will be curved in a opposite directions (because the sign of the charge `q` in the denominator is different in the two cases) , the radius of curvature will be the same.
Thus the correct answer is C) Both are equally curved.
b) is the true