In the figure a small, nonconducting ball of mass m = 0.99 mg and charge q = 2.1 × 10-8 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle 0 = 37° with a vertical, uniformly charged nonconducting sheet (shown in cross section). Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surfaçe charge density o of the sheet. m, q i Units Number

In the figure a small, nonconducting ball of mass m = 1.1 mg and charge q = 2.0 × 108 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle 0 = 30° with a vertical, uniformly charged nonconducting sheet (shown in cross section). Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density of the sheet. + + + + + + + + + + + + + O a

A -198.7 mC charge is placed at the center of a hollow conducting sphere. Find the Charge density (in C/m²) on the outside of the sphere if its radius is 6.47 cm and if it Contains zero net charge.

345 159 A-140.1 mC charge is placed at the center of a hollow conducting sphere. Find the charge density (in C/m²) on the outside of the sphere if its radius is 5.09 cm and if it contains zero net charge.

A coaxial cable consists of a wire of radius a surrounded by a thin metal cylin-drical shell of radius b. The wire has a uniform linear charge density λ >0 and the outer shell has a uniform linear charge density−λ. ( a) Sketch the field lines for this cable. (b) Find expressions for the magnitude of the electric field in the regionsr

A solid insulating sphere of radius a = 5.1 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density p = -224 µC/m³. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b = 13.3 cm, and outer radius c = 15.3 cm. P(40) 1) What is Ex(P), the x-component of the electric field at point P, located a distance d = 34 cm from the origin along the x-axis as shown? N/C Submit + 2) What is V(b), the electric potential at the inner surface of the conducting shell? Define the potential to be zero at infinity. V Submit +) 3) What is V(a), the electric potential at the outer surface of the insulating sphere? Define the potential to be zero at infinity. Submit 4) What is V(c) - V(a), the potentital differnece between the outer surface of the conductor and the outer surface of the insulator? Submit 5) A charge Q = 0.0593µC is now added to the conducting shell. What is V(a), the electric potential at the outer…

A solid block of copper, which is a good conductor, has a cavity in its interior. Within the cavity, insulated from the conductor, is a point charge of +3.00 nC. The block of copper itself has an excess charge of -8.00 nC. How much charge is on (a) the outer surface of the block and (b) the surface of the cavity?

Two isolated metallic solid spheres of radii R and 2R are charged such that both of these have same charge density σ. The spheres are located far away from each other, and connected by a thin conducting wire. Find the new charge density on the bigger sphere.

A charge q = 1 μC is located at the tip of a hollow cone (such as an ice cream cone without the ice cream) with surface charge density o = 6.4 μC/m². The slant height of the cone is L = 4 mm, and the half-angle at the vertex is 0: 10⁰. = L12 L/2 If the top half of the cone is removed and thrown away, what is the force (in Newton's) on the charge 9 due to the remaining part of the cone?

In part (a) of the figure an electron is shot directly away from a uniformly charged plastic sheet, at speed vs = 3.60 x 105 m/s. The sheet is nonconducting, flat, and very large. Part (b) of the figure gives the electron's vertical velocity component v versus time t until the return to the launch point. What is the sheet's surface charge density? Assume ts = 28.0 ps. (a) v (105 m/s) t (ps) (b)