A thin plastic rod of length d =1.5 m lies along the x-axis with its midpoint at the origin. The rod carries a uniform charge density of?= 3.5 nC/m. The point P is located along the y-axis at (0,y = 95 cm).

Part (a)Enter an expression for the electric potential at point P due to a small segment of the rod, of thickness dx, located at (x,0). Give a symbolic answer in terms of ?, x, dx, y, and the Coulomb constant k_e.

Part (b)Using the expression you entered in part (a), choose the correct limits for the integral that will give the electric potential at P.

-d/2 to 0	0 to d	0 to d/2	-d to 0
-d to d	-d/2 to d/2

Part (c)Calculate the electric potential at P, in volts.

3. A parallel-plate capacitor of capacitance C has plate area A and distance between plates d. The capacitor is connected to a battery with voltage V, fully charged and then disconnected. A slab of dielectric material with a dielectric constant of 4.0 is then inserted into capacitor, completely filling region between plates.

Part (a)After inserting the dielectric, the capacitance is now:

C/2	2C	C	C/4
4C

Part (b)After inserting the dielectric, the voltage across the capacitor is now:

V/2	2V	V	4V
V/4

Part (c)After inserting the dielectric, the charged stored in the capacitor is now:

VC/2	2VC	4VC	VC/4
VC

Part (d)After inserting the dielectric, the electric field in the capacitor is now:

Half as large.	Twice as large.	Four times as large.
The same.	One-fourth as large.

4. Capacitors C1 and C2 are connected, as shown, with voltage source V0. Let C1=3.1 F, let C2=6.7 F, and let V0=10.75V.