Saved Bookmarks
| 1. |
A circle, having radii 'a' has line charge distribution over its circumference having linear charge densitylambda = lambda_(0)cos^(2)theta. Calculate the total electric charge residing on the circumference of the circle. [Hint: int_(0)^(2pi)cos^(2)d theta =pi] |
Answer» Solution :The length of an INFINITESIMALLY SMALL lint element shown in fig. is ADD, then the CHARGE or the line element is  `dq = lambda AD theta (therefore lambda = q/l)` `therefore dq = lambda_(0)cos^(2)theta.d theta`………(i) `(therefore lambda = lambda_(0)cos^(2)theta)` In order to calculate the total charge Q residing on the surface, we have to intigrate dq over the entire surface `therefore Q = int_(0)^(2pi) lambda_(0)cos^(2)theta.d theta` `=alambda_(0) int_(0)^(2pi)cos^(2)theta.d theta` `therefore Q = alambda_(0)pi``(therefore int_(0)^(2pi)cos^(2)theta d theta = pi)` |
|