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Hello. I need some help with the following problems.

4. A solid spherical container has a radius of 15 cm. The electric field 30 cm from the center of this sphere has a magnitude of 800 N/C. What is the surface charge density (sigma) on the sphere?

I did:

EA= q/ e0

E(4)(pi)(r^2) = [sigma(4)(pi)(r^2)] / e0

E= sigma / e0

800(8.85 X 10^-12) = sigma

sigma = 7.08 X 10^-9

But the answer is 2.8 X 10^ -8 C/m^2

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6. A uniform line charge of linear charge density lambda= 5 nC/m extends from x=0 to x=10 m. The magnitude of the electric field at the point y=12 m on the perpendicular bisector of the finite line of charge is?

I did:

I made a right triangle where 10 m was the length of the horizontal side and 12 m was the length of the vertical side. Then I found the hypotenuse to be 15.62 m

E= lambda / [(2pi)(e0)(r)]

E= (5X 10 ^ -9) / [(2pi)(8.85 X10^-112)(15.62)

E=7.49

But the answer is 2.88 N/C

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

16. An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density sigma = 12 nC/m^2. The electric field at r = 6.1 cm is approximately?

I did:

EA = q/e0

E(2)(pi)(r)(l) = [sigma(2)(pi)(r)(l) ] / e0

E= sigma / e0

E= 1355.93

But the answer is 1.3 kN/c

I don’t know if my answer is wrong or correct because of rounding.

Any help would be greatly appreciated.

Thanks

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# Homework Help: Ctrostatics, Gauss’s Law, and Potential

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