Question

1) What is E_y(R), the y-component of the electric field at point R, located a distance d = 44 cm from the origin along the y-axis as shown?

2) What is V(P)

Answer 1

so first you have to change p(rho) into a charge. by times it by the area
1.
Q=p*a^2*pi
then
E(R)=((lamda)+Q)/(r*2*pi*8.85e-12) , r= .44m

2.
Use Pythagorean theorm for point P to get your distance sqrt(.44^2+.44^2)
then
V(P)-V(R)= (((lambda)+Q)/(2*pi*8.85e-12))ln(P) - (((lambda)+Q)/(2*pi*8.85e-12))ln(R) ,where R= .44m

3. ok so you have to take the integral from a to b of just the inner cylinder.
-(Q/(2*pi*8.85e-12))integral(a to b) of (1/r)dr

4. 0= (lambda+(rho*a^2*pi))/(2*pi*r*8.85e-12)
solve for rho