There infinitely long charge sheets are placed at planes. z = -a with surface charge density (- o). z = a with surface charge density (-20) and z 3a with surfac

sir. in first case how will u put a (-k)

See for every plate direction of electric field at point P is towards down.Up direction is taken as positive z axis so downward direction is -z axis.Notice direction of field is shown in the figure for every plate.For positive plate it emerges from the plate and goes in up and down direction.For negative plate field lines ends at the plate starting from up and down side.

sir, i have a doubt

why, do u given( -z)for first one. it is given positive. right??

yes surface charge density is positive,it means it will repel the test charge at point P. Hence direction of Electric field due to first one will be in opposite direction ie in -z direction. If you still have any doubt,then please ask.

ok

then the other two charge densities are same as given??

suppose the first one in -ve dire then we take it as positive. right??. left ones are same as given in question.

always keep in mind if surface charge density is positive then it will repel and if surface charge density is attractive then it will attract. Keeping this in mind put the negative or plus sign before unit vector.

yes,if the surface charge density on top is negative then it will attract the test charge.Hence direction of Electric field at point P due to this surface will be in positive z direction