IIT JEE , AIEEE Forum - Physics , Electricity - pls-------------- help potential problem

divalli_oct07

there are 2 parallel infinetely long metallic cylinders of radius 'r' each . their axis are seperated by a distance of 'a' units. charge distribution on the 1st cylinder is +ve

and on the 2nd cylinder is -ve

. find the potential difference between the cylinders.

pleaaaase send a detailed solution as i'm not vry good at potentials.

maverick83

please mention the exact pt. at which potential to be found.......

if you mean in middle of both cylinders then answer should be zero...

elessar_iitkgp

The electric field due to an infinitely long cylinder of radius r, at a distance x from its center can be found by Gauss' Law, and is found to be
E =

r/

x away from the cylinder.
Also, the electric field at any point inside the cylinder is zero (using Gauss' Law)

Consider an origin O at any point on the axis of the +vely charged cylinder. Let the X axis start from this point O, perpendicular to the axes of both the cylinder.
Hence, at a point at a distance x from the origin O (outside the cylinder),
E =

r/

x i₊ (-

)r/

(a-x)(-i) =

r/

[1/x + 1/(a-x)]i

Potential difference between the axes of +ve and the -ve cylinder is

V = - _a

⁰ E.dr = - _a

^a-r 0.dr - _a-r

^r E.dr - _r

⁰ 0.dr

V = - _a-r

^r

r/

[1/x + 1/(a-x)]i . dxi = - (

r/

) _a-r

^r [1/x + 1/(a-x)]dx

V = (2

r/

)ln[(a-r)/a]

kamalasai

i think mr.elessar iitkgp is correct

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