Question

You have a hoop of charge of radius R and total charge -Q. You place a positron at the center of the hoop and give it a slight nudge in the direction of the central axis that is normal to the plain of the hoop. Due to the negative charge on the hoop, the positron oscillates back and forth.

Step 1: Clearly show how to use integration to find the z-axis E-field of a ring charge.

Step 2: Place a positron a small distance above the plane of the ring and calculate the period of oscillation.

Answer 1

length solution. de sino linear charge density de A dEase = - 2 = charge Electre Field due to dl dl é ............ chage de = k dr. dq=adlo all de sino component will concell out to each other - Eneta de caso = (kidlauso 22 Enet = KASO .29R = K[A2KR) 7 1 2 3 het e kombit to y \:v=Jr422) re re

charge on position is e=1:6810-19c Force acting on position towards cempre of sing- Feet = Qez d. to (R²+22) 3/2 for very small distance from centre R² +2² ~ R2 => F= (dneome) 2 => ma = (com ors)? (m=positron- as a= (derm) z a&to mass) I sidisplacement comparing with standard equation Pacceleration ATTEOR m. = Time period of oscullaten T= 20 4TER 3 m W2= de. V Qe