Electric Charges and Field (12Acd01)

Sheet 04 Continuous Charge Distributions and Electric Fields.

1. A thin insulating rod of length l carries a uniformly distributed charge Q. Calculate: the electric field intensity due to this rod at a distance r from one end of the rod.
   
   
   Ans: \(E=\frac{1}{4\pi\epsilon_{o}}\frac{Q}{r\left(r+l\right)}\).
   
   
2. A thin semi-circular ring of radius a is charged uniformly and the charge per unit length is \(\lambda\). Find: the electric field at its center.
   
   Ans: \(E=\frac{1}{2\pi\epsilon_{o}}\frac{\lambda}{a}\).
   
   
3. Express: the electric field intensity at any point on the axis of uniformly charged ring.
   
   Ans: \(E=\frac{1}{4\pi\epsilon_{o}}\frac{qx}{\left(x^{2}+a^{2}\right)^{\frac{3}{2}}}\).