two point charges of +16 micro coloumb and -9 micro coloumb are placed 8cm apart in air determine the position of the point at which resultant electric field is zero? Please give detail solution
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Electric field is inversely proportional to radius of gaussian surface right and electric flux is surface integral of E.ds then if electric field is doubled then electric shud also change but it didnt changes can u tell me why ?
actually it depends
see sometimes square of radius is inversely proportional to the electric field
the electric field didn't change cause Qin=0
if its zero then whatever be the radius, field will remain zero
or Qin is constant then also the flux won't change
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It is totally Impossible to get the zero electric field in between of the charges since both the charges are of the opposite nature.
Now, for finding the distance where electric field is zero, let us keep one test charge Q near the smaller charge (9 micro coulomb) which is outside of both the charges at a distance of x cm.
Field due to -9 micro coulomb charge = kQ(9)/(x)²
Filed due to 16 micro coulomb charge = kQ(16)/(8 + x)²
Now, Net field is to be zero,
Therefore, kQ(9)/Q(x)² - kQ(16)/Q(8 + x)² = 0
kQ(9)/Q(x)² = kQ(16)/Q(8 + x)²
9/x² = 16/(8 + x)²
(3/x)² = (4/(8 + x))²
3/x = 4/(8 + x)
24 + 3x = 4x
x = 24 cm.
Thus, at a distance of 24 cm from the 9 micro coulomb charge, net electric field will be zero.
Hope it helps.
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