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A spherical portion has been removed fro...

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inisde the emptied space is

A

zero everywhere

B

nonzero and uniform

C

nonuniform

D

zero only at its center

Text Solution

Verified by Experts


Let us consider a uniformly charged solid sphere without any cavity. Let the charge per unit volume be `sigma` and O be the center of the sphere. Let us consider a uniformly charged sphere of negative charged density `sigma` having its center at o'. Also let OO' be equal to a (fig). let us consider an arbitrary point P in the small sphere. the electric field due to charge on big. sphere.
`vecE=(sigma//3epsilon_(0))overline(OP)`
Also the electric field due to small sphere is
`vecE_(2)=(sigma)/(3epsilon_(0))overline(PO)` ltbr. therefore the total electric field is
`vec(E)=vecE_(1)+vecE_(2)=(sigma)/(3epsilon_(0))[overline(OP)+overline(PO)]=(sigma)/(3epsilon_(0))overline(OO')`
this will have a finite value, which will be uniform.
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