You can make electric field equations for washer shaped objects by neutralizing

Question

You can make electric field equations for washer shaped objects by neutralizing the center portion of a uniformly charged disk (Hint: what could you add to a charged disk to make the center neutral?) The disk shown has a radius of 14.8 cm and the concentration of charge on the surface has a magnitude of 1.21 Times 10-4 C/m2. The center hole has a radius of 9.2 cm. What is the electric field at the site of an object located 4.85 cm out along the axis of the washer? What radius ring will produce the same electric field as the original disk using the original charge? Will it be larger or smaller or the same size? Predict now.

Explanation / Answer

fill in the centre hole with negative and positive charges of the same magnitude. (net charge added remains zero). The amount of positive charge added should be enough to keep the charge density over the whole plate/washer constant. Now this is a situation of two disk one large and one smaller kept concentrically with opposite charges. For the bigger disk Rbig= 14.8 cm= 0.148m s=1.21*10^-4 C/m2 electric field at a distance 4.85 cm (using formula Field due to bigger disk. Ebig=+5.235 *10^-4 N/C similarly for the smaller disk Rsmall=9.2 cm s= - 1.21*10^-4 C/m2 (charge is negative on this disk) field due to this disk Esmall=-4.057*10^-4 N/C net field Enet=Esmall+Ebig =1.17*10^-4 N/C b) A full disk required to produce this amount of field will be smaller, because all the field produced by that disk will be additive, no negation will be produced. Calculating the disk size by using the same formula and the same charge density we get. Rnew disk = 3.068m

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