Calculate the electric field at height h above the center of a square plate of size 2a x 2a with uniform surface charge density n (both direction and magnitude). Verify that in the limit of large a the result agrees with the field of an infinite uniformly charged plane.

A long line carrying a uniform linear charge density+50.0 mC/m runs parallel to and 10.0 cm from the surface of alarge, flat plastic sheet that has a uniform surface charge density of-100 mC/m2 on one side. Find the location of all points where ana particle would feel no force due to this arrangement of chargedobjects.

An infenitely long and thin-shelled hollow insulating cylinder has a radius R and is uniformly charged wiht a uniform surface charge density ρ. At its central axis is an infinite line iwth linear charge density λ. What is the electric field as a function of radius r. Including answers for r < R and r > R

A long thin straight conducting wire had a uniform like charge density of gamma. It is surrounded by a rubber insulating layer of radius a. Find the electric displacement everywhere and the electric field for r>a.

A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge, of positive charge q.  What is the total surface charge qint_int on the interior surface of the conductor (i.e., on the wall of the cavity)?

A thin glass rod is bent into a semicircle of radius R. A charge +Q is uniformly distributedalong the upper half, and a charge –Q is uniformly distributed along the lower half as shown in the figure. Find the magnitude and direction of the electric field E (in component form) at point P, the center of the semicircle.

Sections AB and CD of a thin non-conducting ring of radius R areuniformly (with constant linear density) charged with charge + q and−q, respectively. The points ABCD form the vertices of the square. Findthe electric field in the center of the ring.

A non-uniform thin rod is bent into an arc of radius R. The linear charge density λ of the rod depends on θ and is given byλ= λ0/cos θwhere λ0 is a positive constant. The arc extends from θ = π/2 to θ = 3π/2  Sketch the direction of the resultant electric field at the origin.Calculate the magnitude of the electric field E⃗ .

The field generated by three uniformly charged infinite flat platesConsider three large parallel plates: plates A and B each carry a surface charge density of 4 nC/m^2. (a) What must be the surface charge density of plate C for the electric field to be zero in region iii? (b) What is then the electric field in region iv (modulus and orientation)?