Consider a charge -q located a small distance z above the center of a positively а. charged ring with total charge +Q and radius R (see example 23.4). Define a coordinate system and draw a pictorial representation of this physical situation. Clearly label any quantities of interest on your diagram. b. Determine the net force exerted on the charge -q due to the positively charged ring. What is the magnitude of the force on the charge -q if it is at the location z = 0? Solve: Use the binomial expansion as a mathematical tool to understand the motion of the charged particle under the assumption that it is only displaced a small distance z « R away from the center of the ring. The binomial approximation to first order is written: с. (1+x)" z 1+ nx if x « 1 Using the binomial approximation, simplify your expression from part (b). You should have two terms in your expression for the net force. Hint: It may be helpful to factor the denominator such that it is in a form (1 + x)" where x is a small quantity composed of variables from the problem.

Consider a charge -q located a small distance z above the center of a positively а. charged ring with total charge +Q and radius R (see example 23.4). Define a coordinate system and draw a pictorial representation of this physical situation. Clearly label any quantities of interest on your diagram. b. Determine the net force exerted on the charge -q due to the positively charged ring. What is the magnitude of the force on the charge -q if it is at the location z = 0? Solve: Use the binomial expansion as a mathematical tool to understand the motion of the charged particle under the assumption that it is only displaced a small distance z « R away from the center of the ring. The binomial approximation to first order is written: с. (1+x)" z 1+ nx if x « 1 Using the binomial approximation, simplify your expression from part (b). You should have two terms in your expression for the net force. Hint: It may be helpful to factor the denominator such that it is in a form (1 + x)" where x is a small quantity composed of variables from the problem.