If there is a a non-uniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−4r/3R)f or r≤R ρ(r)=0 for r≥R where ρ0 is a positive constant. What is the expression for the electric field in the region r <= R?

Use Gauss's law to find the electric field at the field point in the following case. The distance between the field point and the surface of the conductor is d. A semi-infinitely large conductor with surface charge density o. Field point d х Conductor

A point charge q = -5.5x 10 C is placed at the center of a spherical conducting shell of inner radius 2.8 cm and outer radius 3.3 cm. The electric field just above the surface of the conductor is directed radially outward and has magnitude 9.0 N/C. (a) What is the charge density (in C/m2) on the inner surface of the shell? C/m² (b) What is the charge density (in C/m2) on the outer surface of the shell? C/m² (c) What is the net charge (in C) on the conductor?

A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−r/R) for r≤R ρ(r)=0for r≥R where ρ0=3Q/πR3 is a positive constant. Electric field for this charge distribution is  E(r)= kQ/r2 for r≥R kQ/r2 [4(r3/R3) − 3(r4/R4)] for r≤R   a) Show that for r≥R the potential is identical to that produced by a point charge Q. (Take the potential to be zero at infinity.) b) Obtain an expression for the electric potential valid in the region r≤R.

A long nonconducting cylinder (radius 6.0 mm) has a nonuniform volume charge density given by ar, where a= 6.2 mC/m' and r is the distance from the axis of the cylinder. What is the magnitude of the electric field at a point 2.0 mm from the axis?

Calculate the electric field in N/C at point P, a distance (4.35x10^1) cm along the central axis of a disk of charge with radius (9.157x10^0) cm, and charge density +(8.0860x10^0) µC/m2. You do not need to enter a unit vector in your answer, but must put a negative sign in, if the electric field is pointing along the negative z-axis. R