Saved Bookmarks
| 1. |
Four charges of +q, +q, +q and +q are placed at the corners A, B, C and D of a square of side a. Find the resultant force on the charge at D |
|
Answer» SOLUTION :Let SIDE `=a, BD = sqrt2a` Along AD FORCE `F_(1) = (1)/(4pi in_(0)) .(q^(2))/(a^(2))` Along CD force `F_(2) = (1)/(4pi in_(0)).(q^(2))/(a^(2)) therefore F_(1) = F_(2)` Resultant of `F_(1) and F_(2) = SQRT(F_(1)^(2) + F_(2)^(2))= sqrt2.F_(1)` Force along BD `F_(3) = (1)/(4pi in_(0)) .(q^(2))/((sqrt2a)^(2)) = (1)/(2) (1)/(4pi in_(0)) (q^(2))/(a^(2))` Resultant force at `D= sqrt2F_(1) + F_(3)` `= sqrt2 (1)/(4pi in_(0)) .(q^(2))/(a^(2)) + (1)/(2) (1)/(4pi in_(0)).(q^(2))/(a^(2))` `=(1)/(4pi in_(0))(q^(2))/(a^(2)) [sqrt2 + (1)/(2)] = (q^(2))/(8pi in_(0)a^(2)).[1 + 2 sqrt2]` 
|
|