Volume charge density and potential difference in sphere

[fight_club_alum]

Homework Statement

The charge of uniform density 50 nC/m3 is distributed throughout the inside of a long nonconducting
cylindrical rod (radius = 5.0 cm). Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod) and point B (4.0 cm from the axis).

a . 2.7 V

b. 2.0 V

c. 2.4 V

d. 1.7 V <--THE ANSWER

e. 3.4 V

Homework Equations

pr/3Eo = E
E * r = V

The Attempt at a Solution

E=pr/3Eo
v=ER
v=prR/3Eo
v1-v2=prR1/3Eo-prR2/3Eo
= 37.646

 

[TSny]

The electric field is a function of r. So, finding the potential difference ΔV from E will require integration.

 

[TSny]

pr/3Eo = E

Is this the correct formula for inside a cylinder?

 

[fight_club_alum]

Is this the correct formula for inside a cylinder?

I don't think so but I attempted anything because I just wanted to try
May you please show and explain to me how to get the right answer because this is my first example of this kind?
Thank you

 

[TSny]

Try using Gauss' law to find the electric field as a function of r inside the cylinder.

 

[fight_club_alum]

Try using Gauss' law to find the electric field as a function of r inside the cylinder.

E A = Q/eo
E (2piRah) = P * (pi * r^2 * h)/eo
E (2Ra) = P * (r^^2) / eo
E = P* (r^2) / (eo * 2 r_a)
Ea = 353
Va = 353 * 0.02 = 7.06
Vb = 7. 06
I keep getting a wrong answer

 

[TSny]

E A = Q/eo
E (2piRah) = P * (pi * r^2 * h)/eo
E (2Ra) = P * (r^^2) / eo

It is not clear what Ra stands for. But you are on the right track. Hopefully, you drew a diagram in which you have constructed your Gaussian surface. What shape did you choose for the Gaussian surface?

Ea = 353
Va = 353 * 0.02 = 7.06

This is not the correct way to get the potential at point a. You are looking for the potential difference ΔV = Vb - Va. You can find this without having to determine V_b and V_a individually. You should have covered the basic relationship between ΔV and E.

See first equation here:
http://slideplayer.com/slide/903141...gral+of+electric+field+along+a+close+path.jpg