Part A What is the electric field outside the cylinder ( r > R )? Give your answ
ID: 1289331 • Letter: P
Question
Part A
What is the electric field outside the cylinder (r>R)?
Give your answer in terms of the variables ?, r, and R. Combine all numerical values together into one numerical multiplier.
E outside = ?
Part B
What is the potential difference between a point at radius r and the surface of the cylinder?
Give your answer in terms of the variables ?, r, and R. Combine all numerical values together into one numerical multiplier.
different in V = ?
An infinitely long cylinder of radius R has linear charge density Part A What is the electric field outside the cylinder (r>R)? Give your answer in terms of the variables ?, r, and R. Combine all numerical values together into one numerical multiplier. E outside = ? Part B What is the potential difference between a point at radius r and the surface of the cylinder? Give your answer in terms of the variables ?, r, and R. Combine all numerical values together into one numerical multiplier. different in V = ?Explanation / Answer
E_r * 2?r?L = Q / ?_0
where Q = ? ? dV, where V is the volume of interest. I'd imagine your volume to be that which comprises the Gaussian surface used above (i.e. with length ?L)
Q = ? (going from 0 to r) ? 2?r?L dr
Q = ? ? r^2 ?L
E_r = ? ? r^2 ?L / ?_0 2?r?L
E_r = ? r / ?_0 2
ED = (?_0 / 2) (? r / ?_0 2)^2
ED = (? r)^2 / 8 ?_0
total E field energy per u. l. = ? (going from r_a to r_b) [ (? r)^2 2?rL / 8 ?_0 ] dr