A vertical cylinder of radius R& length L contains a charge Q uniformly distribu

Question

A vertical cylinder of radius R& length L contains a charge Q uniformly distributed throughout its volume. The flux through the curved side of the cylinder is 3Q/46,. What is the flux through the top end of the cylinder? 30. A charge of 8.0 pC is distributed uniformly on a spherical surface (radius 2.0 cm), and a second charge of-3.0 pC is distributed uniformly on a concentric spherical surface( Determine the magnitude of the electrie field 5.0 cm from the center of the two surfaces. Ans: 18N/C

Explanation / Answer

29. A verical cylinder of radius R, length L conatins charge Q, uniformly distributed over its volume

so volume charge density, rho = Q/pi*R^2*L

total flux through the cylinder = Q/epsilon

flux through the curved sides = 3Q/4epsilon

hence flux through top and bottom sides = Q/epsilon - 3Q/4epsilon = Q/4*epsilon

from symmetry, the top and bottom surfaces have same flux leaving through them

hence flux through top end of the cylinder = Q/8*epsilon

30. charge q = 8*10^-12 C

uniformly distributed over spherical surface , radius r = 0.02 m

charge Q = -3*10^-12 C

uniformly distributed over spherical concentric surface R = 0.04 m

electric field at r = 5 cm = 0.05 m from the center of the two spheres is E

the from gauss' law

E*4*pi*r^2 = (q + Q)/epsilon

E = k(q + Q)/r^2 ( where k is coloumbs constant)

E = 8.98*10^9(5*10^-12)/0.05^2 = 17.96 V/m

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