Physics 272. Midterm I

Please write your name at the top of the page There are 4 problems. Each is assigned 25 points. Show your work.

Problem 1: 25 points
Charges are located on the corners of a square as shown in the Figure. Here C and a=5.0 cm

(a) Find the force on the charge at the lower left. Give the result in component form.
(b) Find the electric field on the charge at the lower left. Give the result in component form.

Problem 2: 25 points
A very large flat plate with unknown surface charge density is placed on a horizontal table. A cork ball of mass m=1.55 g carrying a charge of C remains motionless a constant distance above the plate.

(a) Draw a sketch of this situation.
(b) What force balances the force of gravity and allows the cork ball to remain motionless above the plate ?
(c) What is the charge density on the plate. (Hint: what is the E field of an infinite charged plane ?)

Problem 3: 25 points
Two long thin cylindrical shells of radii and are oriented coaxially (one cylinder is centered on the other). The inner cylinder (radius ) carries linear charge density . The outer cylinder carries linear charge density . (This is a simple model of a coaxial cable used to transmit signals).

(a) Draw a sketch of this situation.
(b) What is the electric field outside both cylinders as a function of r ?
(c) What is the electric field inside both cylinders as a function of r ?
(d) What is the electric field in the region between the cylinders as a function of r ?

Problem 4: 25 points
Charge is distributed throughout a sphere of radius R with non-uniform charge density

and

and

where is a constant.

(a) Draw a sketch of the charge density versus r.
(b) What is the total charge inside the sphere.
(c) What is the electric field outside the sphere ?