- #1

- 407

- 0

1. A line with a charge of density -2uC is on the x-axis starting at point x=1m to x=3.5m. Find its charge density and derive an expression for the magnitude and direction of the electric field at a point situated at x=-1.5m.

Ok so here's what I did:

E=[tex]\int[/tex](KDQ)/r^2

I did [tex]\lambda[/tex]=dQ/dL and dQ=(Qdx)/2.5 (2.5 is the length of the line)

I took the limits to be 1 to 3.5, and r^2=2.5^2=6.25

So E=KQ/(2.5x6.25)[tex]\int[/tex]dx ...with limits 1 to 3.5

so E=KQ/15.6 (3.5-1), the final answer I got was 2.88x10^4 N/C, and the direction is left.

Is that right? if it isn't what do I change?

2. An insulating spherical shell with an inner radius 0.1 cm and outer radius 0.3 cm carries a total charge of 20 nC. Use Gauss's law to find an expression for the electric field at a distance r=0.08cm, r=0.2cm, r=0.4cm.

So what I did was [tex]\phi[/tex]=[tex]\int[/tex]EdA = Qin/E0.....integral of dA is A and A=4[tex]\Pi[/tex]r^2....

So then I did E=20nC/(4[tex]\Pi[/tex]r^2E0)...and I plugged in the different radii...however this is wrong, or most of it anyway, can someone help please?

3. An arc length with a length of 6 cm and a radius of 3cm carries a uniform charge of 10nC. Derive an expression for the magnitude and direction of electric field at the center.

I don't know what to do for this one. Am I suppose to integrate? like E=[tex]\int[/tex](KdQ)/r^2...

Thanks a lot for any help :)