The electric potential at x = 3.0 m is 120 V, and the electric potential at x = 5.0 m is 190 V. What is the electric field in this region, assuming it's constant?

A capacitor with plates separated by distance d is charged to a potential difference $\Delta V _ { C }$. All wires and batteries are disconnected, then the two plates are pulled apart (with insulated handles) to a new separation of distance 2d. a. Does the capacitor charge Q change as the separation increases? If so, by what factor? If not, why not? b. Does the electric field strength E change as the separation increases? If so, by what factor? If not, why not? c. Does the potential difference $\Delta V _ { \mathrm { C } }$ change as the separation increases? If so, by what factor? If not, why not?

A cart moving to the right passes point 1 at a speed of 20.0 m/s. Let g=9.81

$$m/s^2$$

. (a) What is the speed of the cart as it passes pint 3? (b) Will the cart reach position 4? Ignore friction.

In Figure 17.78 a proton is moving upward with speed $5 \times 10^6$m/s. What is the magnetic field due to this moving proton at the indicated locations? Each location is a distance r = 8 cm from the proton. Give both magnitude and direction of the magnetic field at each location.

An electron with an initial speed of 500,000 m/s is brought to rest by an electric field. a. Did the electron move into a region of higher potential or lower potential? b. What was the potential difference that stopped the electron?

The potential at the surface of the sphere (radius $R$) is given by

$$V_0=k\cos3\theta$$

where $k$ is a constant. Find the potential inside and outside of the sphere, as well as the surface charge density $\sigma(\theta)$ on the sphere. (Assume there's no charge inside or outside of the sphere)