A hollow metal sphere has an inner radius a and outer radius b. The hollow sphere has charge +2 Q. A point charge + Q sits at the center of the hollow sphere. Determine the magnitude of the electric field in the region r≤a.

Light traveling in a medium with a refractive index 1.19 is incident on a plate of another medium with index of refraction 1.79. at what angle of incidence is the reflected light fully polarized?

The scalar triple product computes the magnitude m of the moment of a force vector f about a specified line. it is m = (r × f) · n, where r is the position vector from the line to the point of application of the force and n is a unit vector in the direction of the line. use matlab to compute the magnitude m for the case where f = [12, −5, 4] n, r = [−3, 5, 2] m, and n = [6, 5, −7].

Aspring with an unstrained length of 0.071 m and a spring constant of 2.6 n/m hangs vertically downward from the ceiling. a uniform electric field directed vertically upward fills the region containing the spring. a sphere with a mass of 5.29 10-3 kg and a net charge of +7.2 µc is attached to the lower end of the spring. the spring is released slowly, until it reaches equilibrium. the equilibrium length of the spring is 0.058 m. what is the magnitude of the external electric field?