InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
(a) Write two properties by which electric potential is related to the electric field . (b) Twopoint chargesq_(1) and q_(2)separated by a distance of r_(12) are kept in an external electric field. Derive an expression for the potential energy of the system of two charges in the field. |
|
Answer» Solution :(a) From the relation `E =-(dv)/(dr)` (i)The magnitude of ELECTRIC field intensity is numerically equal to potential GRADIENT. (ii) Negative sign signifies the electric field intensity is in the direction of decreasing electric potential gradient. Consider a system of two point charge `q_(1) and q_(2) " such that " q_(2)` is intially far away from `q_(1)` in free space. Charge `q_(1)` PROVIDES necessary electric field all around it work is done to bring charge `q_(2)` from infinity to point B near A,` W= q_(2) V, ` V is potential at B due to `q_(1)` Also` V=1/(4pi in_(0))(q1)/(AB) rArr W=1/(4pi in _(0)) (q_(1)q_(2))/(AB),AB=|vec(r_(2))-vec(r_(1))|` `W_(1) = 1/(4pi in _(0)) (q_(1) q_(2))/(|vec(r_(2))-vec(r_(1))|)=1/(4piin_(0))(q_(1)q_(2))/(r_(12))` If `vec(E)_(r)` External electric field then the work -done to bring the CHARGES `q_(1) and q_(2)` to their position from the infinity are `W_(2)=q_(1)(r_(1)) E_(1) and W_(3)=q_(2)(r_(2))E_(2)` `:. " Total work done "W= w_(1) + w_(2) + w_(3)` `U=1/(4pi in_(0)) (q_(1)q_(2))/(|vec(r_(1)) -vec(r_(2))|)+q_(1)(r_(1))E + q_(2) (r_(2)) E` 
|
|