Using a symmetry argument, explain why, for points on the positive z-axis, the gravitational field points towards the centre of the disk, i.e. parallel to the z-axis. Starting from the gravitational potential, and using the answer to 4., derive an expression for the gravitational field a for points on the positive z-axis. What does this become in the limit R → 0? (Brain teaser) Show that the potential o “becomes infinite" in that same limit. How can you get round this problem, to find the gravitational field from the potential even in the limit R→ 0?

electron in a well. digure 24-65 shows eletric potential V along an x axis. the scale of the vertical axis is set by Vs=8.0V. An eletron is to be released at x=4.5 cm with intial kinetic energy 3.00eV. (a) if it is initially moving in the negative direction of the axis, does it reach a turning point (if so. what is the x coordinate of that point) or does it escape from the plotted region (if so, what is it its speed at x=0)? (b) if it is initially moving in the posiitve direction of the axis, does it reach a turning point (if so, what is the x coordinate of that point) or does it escape from the plotted region (if so, what is its speed at x=7.0 cm)? what are the (C) magnitude F and (d) direction (positive or negative direction of the x axis) of the electric force on the electron if the electron moves just to the left of x=4.0 cm? What are (e)F and (f) the direction if it moves just to the right of x=5.0cm?

radius R (uniformly distributed) are located at z = R and z =-R and have the same (z) axis. (a) Find expressions for the total electric potential at the origin (z = 0), at the center of the ring at z = R, and at a point on the z axis a distance from the origin, where 0 < z < R. (b) A small bead of mass m with charge q is threaded on a frictionless string along the z axis. If the bead is released from rest at z, will it move toward the origin or toward the ring at z = R? (c) Find an expression for the speed of the bead as it passes through the point you picked in (b).

A thin rod has uniform charge per length 3w over its length H. The distance between point A and point B is 3H and the distance between point A and point P is 2H. We introduce an integration variables with 5 = 0 chosen to be at point A and the +s direction to be down. The small red segment has length ds and charge dg. We want to find the electric potential at point P. Draw it out--label the all the lengths and the integration variable! A. dV= B. dV C. dV = D. dV= A Which expression below gives the voltage d'V from the small charge dg in the small segment ds? Choose from the choices (A thru F) below: E. dV= F. dV= B с Kdq √√²+4H² Kdg (s² +4H²) Kdq 5 Kdq √(8+3H)² +4H² Kdg ((s+3H)² +4H²) 3.Kdq H ((8+6H)² +97²)³/2 -P +y >+x What are the limits of integration s? [Select] [Select]