1)An infinitely long cylinder is uniformly charged with a volume density of 4 C/

Question

1)An infinitely long cylinder is uniformly charged with a volume density of 4 C/m3. The cylinder has a radius of 5 cm. Calculate the electric field at a distance of 8 m from the axis of the cylinder.(The cylinder is not "conductor")

2)What happens if the distance from the axis is less than the radius? Calculate the electric field at a point 0.2 cm from the axis of the above infinite cylinder.

3)If instead of having a finite radius, the cylinder were an infinite line of charge with the same effective linear charge density as the above cylinder, calculate the electric field at a distance of 8 m from the line of charge. Use a positive sign for the answer if the electric field points radially outward and vice versa.

Explanation / Answer

1)
at r > R

E = rho*R^2/(2*epsilon*r)

= 4*0.05^2/(2*8.854*10^-12*8)

= 7.06*10^7 N/c

2) ar r<R

E = rho*r/(2*epsilon)

= 4*0.002/(2*8.854*10^-12)

= 4.52*10^8 N/c

3) charge per unti length,lamda = rho*A

= 4*(pi*0.05^2)

= 0.0314 C/m

E = lamda/(2*pi*epsilon*r)

= 2*k*lamda/r

= 2*9*10^9*0.0314/8

= 7.065*10^7 N/c

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