A thin plastic rod of length d = 1.3 m lies along the x-axis with its midpoint at the origin. The rod carries a uniform charge density of λ = 9.5 nC/m. The point P is located along the y-axis at (0,y = 55 cm).   Calculate the electric potential at P, in volts.

A long cylindrical insulating shell has an inner radius of a=1.41 m and an outer radius of b=1.6 m. The shell has a constant charge density of 3.5×10−9 C/m3. The picture shows an end-on cross-section of the cylindrical shell. If we take the potential at the axis to be zero, what is the electric potential at the outer radius of the shell?

A dielectric cylinder with absolute permittivity e, has radius b and height L. The bottom plate of the cylinder is positioned at x-y plane, concentric with the z-axis. The polarization vector in the dielectric cylinder is given P = 6Por cos(o), where Po is a constant. Find (a) Bound charge densities (b) The total charge of the cylinder. (C) Write the integral expression of the potential at P (0,0,0) explicitly. Define the integral limits and all the components in the integrant expression. Do not take the integral.

A charged conducting spherical shell of radius R = 3 m with total charge q = 23 μC produces the electric field given by E⃗ (r)={014πϵ0qr2r̂ forforr<Rr>R(PICTURE ATTACHED OF EQUATION) a. Enter an expression for the electric potential inside the sphere ( r < R ) in terms of the given quantities, assuming the potential is zero at infinity.  V(r)= b. Calculate the electric potential, in volts, at radius r inside the charged shell. V(r) =

The electric potential is given by the following expression: V(x, y, z) = x²yz + 2y²z, where V is in volts. Determine the electric field (magnitude and direction) at point (1, 1, 2).

The electric field in a region of space has the components Ey = Ez = 0 and Ex = (4.00 N/C · m) x. Point A is on the y axis at y = 3.60 m, and Point B is on the x axis at x = 4.40 m. What is the potential difference between VB − and VA?

What is the magnitude of the electric field at the point (4.00 î - 9.00 ĵ + 3.90 k̂) m if the electric potential is given by V = 3.20xyz2, where V is in volts and x, y, and z are in meters?

The electric field in a region of space is described by E = <25.0x, 0,0> (N/C). An object moves from an initial lcoation on the y-axis at y = 0.750m to a final location on the x-axis at x = 1.250m. Calculate the change in electric potential.

A capacitor consists of two large flat parallel plates. One plate has surface charge density 4.96 nC/m2 and the other has an equal but opposite surface charge density. The plates are spaced a distance 8.01 cm apart. Give the magnitude of the voltage (difference in electric potential) between the two plates. Answer in units of V.

The thin plastic rod of length L = 18.2 cm in the figure has a nonuniform linear charge density λ= cx, where c= 24.8 pC/m. (a) With V=0 at infinity, find the electric potential at point P₂ on the y axis at y D=4.90 cm. (b) Find the electric field component Ey at P₂. (a) Number i (b) Number i D d- Units V Units V/m