.. A charge of is spread uniformly over the surface of one face of a nonconducting disk of radius.(a) Find the magnitude and direction of the electric field this disk produces at a point Pon the axis of the disk a distance from its centre. (b) Suppose that the charges were all pushed away from the centre and distributed uniformly on the outer rim of the disk. Find the magnitude and direction of the electric field at point P. (c) If the charge is all brought to the centre of the disk, find the magnitude and direction of the electric field at point P. (d) Why is the field in part (a) stronger than the field in part (b)? Why is the field in part (c) the strongest of the three fields?

The electric field due to a uniformly charged disc at a point very close from the surface of the disc is given by, ( σ is the surface charge density of the disc)

Assume axis of disk be +x to get the magnitude of electric filed

Solve from formula

If all the charges is pushed to outer ring then the disc become ring

Solve for ring

The Charge is negative so the electric field line are oriented toward ring and the electric field has only component in x direction so the net field is in

If the Charge is brought together thenit'sconsideredas point charge and the electricfieldmagnitudeis

Therefore if disk become ring then the electric field is

If the disk become point charge then the electric field is

In part (a) charge is distributed over the area so the charge density is large so each differential chargeproduceverticaland horizontalelectricfieldand inthiscase the thehorizontalelectricfieldis small so the netfieldisrelativelystrongbut in part (B)verticalcomponent the chargedensityis small aswellas the electric fieldgeneratedso the net field issmall

in part (a) and (b) thefieldverticalcomponentarecancelledeach other so the fina; net field is thehorizontalfield and this may beconsideredas loss in thefieldbut in part (C) the charge produce the filed without any loss because the charge has only one strongcomponent

Therefore ,Because of charge density and due to the losses in the field part (a) stronger than the field in part (b) and (c) is the strongest one