A metal sphere of radius 15 cm has a net charge of $3.0 \times 10^{-8} C$. What is the electric field at the sphere’s surface?

Establish each identity. $\cos (\pi-\theta)=-\cos \theta$

Give the slope of any line that is (a) parallel to, and (b) perpendicular to, the graph of the given equation. y=5(x+1)

The cable supports the three loads shown. Determine the sags $y_B$ and $y_D$ of points B and D. Take $P_1$=4 kN, $P_2$=2.5 kN.

A 35-kg child stands on the edge of a playground merry-go-round that has a radius of 2.0 m and a rotational inertia of $500 \mathrm { kg } \cdot \mathrm { m } ^ { 2 }$. The merry-go-round has a rotational speed of $0.20 \mathrm { s } ^ { - 1 }$ when the child is standing still. If the rotational speed increases to $0.25 \mathrm { s } ^ { - 1 }$ when the child starts walking along the edge, with what speed is he walking in the reference frame of the merry-go-round, and in which direction?

At a sale, Salazar bought 4 T-shirts and 3 pairs of jeans for $181. At the same store, Jenna bought 1 T-shirt and 2 pairs of jeans for$94. The T-shirts were all the same price, and the jeans were all the same price. Solve the system.

A hollow metal sphere has a potential of +400 V with respect to ground (defined to be at V = 0) and a charge of

$$5.0 × 10^-9 C$$

. Find the electric potential at the center of the sphere.

A neutral solid metal sphere of radius 0.1 m is at the origin, polarized by a point charge of $6 \times 10^{-8}\ \mathrm{C}$ at location $\langle- 0.3,0,0\rangle\ \mathrm{m} .$ At location $\langle 0,0.07,0\rangle\ \mathrm{m},$ what is the electric field contributed by the polarization charges on the surface of the metal sphere? How do you know?

What is the escape speed for an electron initially at rest on the surface of a sphere with a radius of 1.0 cm and a uniformly distributed charge of

$$1.6 × 10^-15 C$$

? That is, what initial speed must the electron have in order to reach an infinite distance from the sphere and have zero kinetic energy when it gets there?

What are the (a) size and (b) direction (up or down) of current $i$ in Fig., where all resistances are $4.0 \Omega$ and all batteries are ideal and have an emf of $12 \mathrm{~V}$ ? (Hint: This can be answered using only mental calculation.)

Two isolated, concentric, conducting spherical shells have radii $R_1 = 0.500$ m and $R_2 = 1.00$ m, uniform charges $q_1 = +2.00 \mu$C and $q_2 = +1.00 \mu$C, and negligible thicknesses. What is the magnitude of the electric field E at radial distance r = 4.00 m?

Two long, charged, thin-walled, concentric cylindrical shells have radii of 3.0 and 6.0 cm. The charge per unit length is $5.0 \times 10^{-6}$ C/m on the inner shell and $-7.0 \times 10^{-6}$ C/m on the outer shell. What is the magnitude E of the electric field at radial distance r = 4.0 cm?

What is the electric potential energy of two electrons separated by 2.00 nm?

The thin plastic rod of length L=10.0 cm in given figure has a nonuniform linear charge density $\lambda=c x$, where $c=49.9 \mathrm{pC} / \mathrm{m}$. Why cannot the field component $E_x$ at $P_2$ be found using the result of of earlier exercise?