Question

Please show the FORMULA first and then solve for values

(1 point) THE PROBLEM A cylinder of radius R-1 cm and length L-49 cm has charge Q-2.2 pC spread uniformly along its surface (and not on its flat ends). (a) Calculate the electric field strength a distance d-4 mm from the cylinder's surface (not near either end). (b) Calculate the electric field strength a distance D-24 m from the rod PAPER SOLUTION INTERPRET Identify all of the true statements. A. To an excellent approximation, an infinitely long rod would give the same result for part (a) in a real-life experiment. B. Very close to the rod (not near either end), the ends have a tiny effect on the electric field C. Far away from the rod, the rod's shape has a tiny effect on the electric field. D. None of the above. DEVELOP If needed, please use k rather than co. (a) Derive a simple practical algebraic expression for the field strength at d (b) Derive a simple practical algebraic expression for the field strength at D. EVALUATE

Answer 1

Charge density of the cylinder: sigma = Q/Area sigma = Q/2 pi R L sigma = 2.2 times 10^-6/2 times 22/7 times (1 times 10^-2) times (49 times 10^-2) sigma = 1/14 times 10^-3 c/m^2 For electric field strength at a distance d = 4mm: Here, d is very very less compared to the length of the cylinder thus: we can take the approximation that the metal cylinder is of infinite length, compared to the point p Therefore E = sigma R/elementof_0 d E = 1/14 times 10^-3 times 1 times 10^-2/1/36pi times 10^-9 times 4 times 10^-3 E = 36 pi/4 times 14 times 10^7 E = 2.02 times 10^17 N/c \r\n Electric field strength at a distance D = 24m from the rod Here D is very large compared to the length of the cylinder Thus we can take the cylinder as a point charge Therefore E = KQ/D^2 E = 9 times 10^9 times 2.2 times 10^-6/24^2 E = 34.375 N/c