Assume that a ball of charged particles has a uniformly distributed negative charge density except for a narrow radial tunnel through its center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton anywhere along the tunnel or outside the ball. Let FR be the magnitude of the electrostatic force on the proton when it is located at the ball's surface, at radius R. As a multiple of R, how far from the surface is there a point where the force magnitude is 0.52FR if we move the proton (a) away from the ball and (b) into the tunnel? (a) Number i (b) Number i Units Units

Determine the magnitude of the electric field at the surface of agold-197 nucleus, which contains 79 protons. Assume that the nucleushas a volume 197 times that of one proton, and consider a proton to be a sphere of radius 1.20 x 10-15 m.

Two identical circular planar surface charges float in free space (permittivity €0). The surface charge density is constant over the disk pso (with units As/m²) for both disks. The disks are separated by distance 'a'. Let's fix the coordinate system such that the upper disk is on the xy plane (z = 0) and its center lies on the origin. The lower plate is on the xy plane (z = −a). The goal is to find the expression for electric scalar potential at the symmetry axis (z) between the two disks. a Ps0 Ps0 Z S O A b (a) Determine the scalar potential V(z) at the z axis in between the two disks. Re- member that you need to integrate the effect of all charge in the disk. (Since there are two disks you will need superposition. The cylindrical coordinate sys- tem should be helpful.) Hint: X (B² + x²)¹/2′ where C is constant of integration. dx = B² + x² + C

A non-conductive plate (thick slice) has a thickness of 2d, which is small compared to its height and width. The origin is in the center of this plate (slice) and the x-axis is along the thickness of this plate. This plate has volumetric charge densities where p (x) = -P in the region where -d <x <0, where po is a positive constant, and p (x) = + Po in the region where 0 <x <+ d. What happens to the electrified vector in the region where x = d / 3?

A thin rod has uniform charge per length z. The distance between point A and point B is 5W and the distance betweer point A and point C is 8W and the distance between point Cand point P is 2W. We introduce an integration variable h with h = 0 chosen to be at point B and the th direction to the left. The small r segment has length dh and charge dq. We want to find the electric field at point P. Draw it out--label the all the lengths and the integration variable! A B C P

A ring and a disk both are centered at (0, 6, 3) and are both lying on the plane y = 6. The ring has a radius of 7 m, while the disk has a radius of 9 m, so that the ring is around the disk. Determine the magnitude of the electric field in kV/m at point (0, -9, 3) if the ring has a total charge of -8 mC and the disk has a total charge of 6 mC. All coordinates are measured in meters.

A proton is held stationary at distance d, from an infinitely large conducting plane (sheet) of charge with uniform charge density -o. It is then released and moves straight towards the plane. Find the speed of the proton when it is at distance d, from the plane. The electric field of the plane is uniform everywhere in space and has the magnitude E = Ignore the gravitational force. Present your answer symbolically.

A spherical shell of radius R carries charge Q uniformly distributed over its surface.   Suppose there is a tiny gap dividing the sphere in two equal halves. Find the force of repulsion between these two halves.

Protons are projected with an initial speed v, -9.65 km/s from a field-free region through a plane and into a region where a uniform electric field E-720) N/C is present above the plane as shown in in the figure below. The initial velocity vector of the protons makes an angle with the plane. The protons are to hit a target that lies at a horizontal distance of R 1.22 mm from the point where the protons cross the plane and enter the electric field. We wish to find the angle at which the protons must pass through the plane to strike the target. Proton beam --720j N/C Target E-0 below the plane G (a) What analysis model describes the horizontal motion of the protons above the plane? O particle under constant velocity O particle under constant acceleration O particle in uniform circular motion O particle in simple harmonic motion (b) What analysis model describes the vertical motion of the protons above the plane? O particle under constant velocity O particle under constant acceleration O…

Suppose you design an apparatus in which a uniformly charged disk of radius R is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point P at distance 2.60R from the disk (see Figure (a)). Cost analysis suggests that you switch to a ring of the same outer radius R but with inner radius R/2.60 (see Figure (b)). Assume that the ring will have the same surface charge density as the original disk. If you switch to the ring, by what part will you decrease the electric field magnitude at P? Number i Units (a) (b)