a) What is E y (R), the y-component of the electric field at point R, located a

Question

a) What is Ey(R), the y-component of the electric field at point R, located a distance d = 42 cm from the origin along the y-axis as shown?

b) What is V(P) – V(R), the potential difference between points P and R? Point P is located at (x,y) = (42 cm, 42 cm).

c) What is V(c) - V(a), the potentital difference between the outer surface of the conductor and the outer surface of the insulator?

d) The charge density of the insulating cylinder is now changed to a new value, ’ and it is found that the electric field at point P is now zero. What is the value of ’?

Explanation / Answer

a)
Here we just use our standard electric field equation for a cylindrical symmetry:

E = 2k*enclosed / r

To find the of the inner cylinder we use the fact that
p = / A
= / pi*r^2

Then enclosed will be inner + outer

b)
dV = kenclosed * ln(R/P)

c)
Moving through the conductor will create no change in potential because the E field is zero. We then
take the integral of the E field moving from the conductor to the insulator and get.

dV = -2kenclosed * ln(A/B)

d)
We know that in order to have an electric field of zero, we need to cancel the effect of the conductor and get a of the same value but opposite sign from the inner cylinder. Using the fact that:
p = /A = /pi*r^2
And using the radius of the insulating cylinder but the of the conductor, we can find the necessary charge density.

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