A unifrom surcace charfge of denstity ` sigma` is given to quarter infinite non conducting place in fist quardrant of ` x-y` plane . Find the z-compounct of the elctric field at the point (0, 0, x) Hence or otherwise find the potential difference between the points (0, 0, d) and (0, 0, 2d)
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Answer

`(sigma)/( 8 varepsilon_0) , (sigmad)/( 8varepsilon__0)`

Explanation

(a) Field due to infinite surface at (0, 0, z)
`vec E = (sigma)/(2 in_0) hat k`

so `z` compnent of field due to quarter part
`vec E = 1/4 ((sigma)/(2 in_0)) hat k`
(b) `int _v^v dV = - int_d^(1d) E_z dz`
`Delta V =- - int_d^(2d) (sigma)/(8 in_0) dx rArr Delta V =- (sigma)/(8 in_0) (Z)_(d)^(2d)`
`Delta V = ( - sigma d)/(8 in_0) dz rArr Deltaa V =- (sigma)/(8 in_0) (z)_pd^(2d)`
`Delta V = (-sigma d)/(8 in_0)`.