If charge is uniformly distributed in xy plane with charge density σ in the first quadrant and -σ in the remaining three quadrants , then work done by electric field in moving a point charge q from (0,0,d) to(0,0,2d). is:

a) -σqd/4ε
b) σqd/4ε
c) -σqd/2ε
d) σqdε




The electric field at a point P due to a charged sheet having uniform charge density σ is given by:

E = σ/2ε * n

where, n is a unit vector normal to the sheet and pointing towards the point P.


For the given charge distribution, the electric field at point (0,0,d) due to the charge in the first quadrant is given by:

E1 = σ/2ε * (0,0,-1)

The electric field at point (0,0,d) due to the charge in the remaining three quadrants is given by:

E2 = -σ/2ε * (0,0,-1)

The total electric field at point (0,0,d) is given by:

E = E1 + E2 = 0


The electric field at point (0,0,2d) due to the charge in the first quadrant is given by:

E1' = σ/2ε * (0,0,-1)

The electric field at point (0,0,2d) due to the charge in the remaining three quadrants is given by:

E2' = -σ/2ε * (0,0,-1)

The total electric field at point (0,0,2d) is given by:

E' = E1' + E2' = 0


The work done by the electric field in moving a point charge q from point (0,0,d) to point (0,0,2d) is given by:

W = q * (ΔV)

where, ΔV is the potential difference between the two points.

The potential difference between the two points is given by:

ΔV = V' - V = -∫E.dr

where, dr is the displacement vector and the integral is taken over the path between the two points.

Since the electric field is zero along this path, the potential difference between the two points is also zero, i.e., ΔV = 0.

Therefore, the work done by the electric field in moving the point charge q from point (0,0,d) to point (0,0,2d) is zero, i.e., W = 0.


The correct option is (d) σqdε. The work done by the electric field in moving the point charge q from point (0,0,d) to point (0,0,2d) is zero.

C) Riya..