91Ó°ÊÓ

What is the electric potential at the point indicated a dot in FIGURE EX25.31?

The electric potential at the dot in FIGURE EX25.32 is 3140 V. What is charge q ?

$x=-1.0cm$$A-2.0nC$charge and a $+2.0nC$charge are located on the x-axis at and $x=+1.0cm$, respectively.

a. Other than at infinity, is there a position or positions on the x-axis where the electric field is zero? If so, where?

b. Other than at infinity, at what position or positions on the x-axis is the electric potential zero?

c. Sketch graphs of the electric field strength and the electric potential along the x-axis.

Two point charges qa and qb are located on the x-axis at x = a and x = b. FIGURE EX25.34 is a graph of V, the electric potential.

a. What are the signs of qa and qb?

b. What is the ratio $qa/qb$?

c. Draw a graph of Ex, the x-component of the electric field, as a function of x.

The two halves of the rod in FIGURE EX25.35 are uniformly charged to {Q. What is the electric potential at the point indicated by the dot?

Two point charges 2.0 cm apart have an electric potential energy -180 mJ. The total charge is 30 nC. What are the two charges?

A -10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis. a. What is the electric potential at the point on the x-axis where the electric field is zero? b. What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

A +3.0 nC charge is at x = 0 cm and a -1.0 nC charge is at x = 4 cm. At what point or points on the x-axis is the electric potential zero?

A proton is released from rest at the positive plate of a parallelplate capacitor. It crosses the capacitor and reaches the negative plate with a speed of $50,000\mathrm{m}/\mathrm{s}$. The experiment is repeated with a${\mathrm{He}}^{+}$ ion (charge $\mathrm{e}$, mass$4\mathrm{u}$ ). What is the ion's speed at the negative plate?

Two protons are launched with the same speed from point 1 inside the parallel-plate capacitor of FIGURE Q25.4. Points 2 and 3 are the same distance from the negative plate.

a. Is $\mathrm{Δ}{U}_{1→2}$, the change in potential energy along the path $1→2$, larger than, smaller than, or equal to $\mathrm{Δ}{U}_{1→3}$?

b. Is the proton's speed $v_2$at point 2 larger than, smaller than, or equal to $v_3$? Explain.