(e) The electric field E at vector r away from a charge q is 이 r E = 4лεr² r where r is the length of the vector. If two positive unit charges, q₁ and 92 are placed at (-0.5, 0, 0) and (0.5, 0, 0) respectively, by summing the vectors obtain the field at (0, 1.5, 0). What is the force experienced by a charge of -2 placed at this position? [4]

A spherical lubber balloon carries a total charge Q distributed uniformly over its surface. At r=0 , the radius of the balloon is R. The balloon is then slowly inflated until its radius reaches 2R at the time t0 . Determine the electric field due to this charge as a function of time (a) at the surface of the balloon, (b) at the surface of radius R, and (c) at the surface of radius 2R. Ignore any effect on the electric field due to the material of the balloon and assume that the radius increases uniformly with time.

Draw the electric field for a system of three particles of charges +1C , +2C , and 3C fixed at the corners of an equilateral triangle of side 2 cm.

On a typical clear day, the atmospheric electric field points downward and has a magnitude of approximately 100 N/C. Compare the gravitational and electric forces on a small dust particle of mass 2.01015 g that carries a single electron charge. What is the acceleration (both magnitude and direction) of the dust particle?

Two parallel plates 10 cm on a side are given equal and opposite charges of magnitude 5109 C. The plates are 1.5 mm apart. What is the electric field at the center of the region between the plates?

A total charge q is distributed uniformly along a thin, straight rod of length L (see below). What is the electric field at P1?AtP2?

A particle of charge q and mass m is placed at the center of a uniformly charged ring of total charge Q and radius R. The particle is displaced a small distance along the axis perpendicular to the plane of the ring and released. Assuming that the particle is constrained to move along the axis, show that the particle oscillates in simple harmonic motion with a frequency f=12qQ40mR3.

Repeat the previous problem, assuming that the electric field is directed along a body diagonal of the cube.

What is the magnitude of the electric field due to a charged particle at its exact location (r = 0)?

Two thin parallel conducting plates are placed 2.0 cm apart. Each plate is 2.0 cm on a side; one plate carries a net charge of 8.0 C , and the other plate carries a net charge of 8.0C . What is the charge density on the inside surface of each plate? What is the electric field between the plates?