GATE EC 1993 Electromagnetics Solution Q 2

# GATE EC 1993 Electromagnetics Solution Q 2

For the uniformly charged sphere of radius R and charge density, \rho the ratio of a magnitude of electric field at distances R/2 and 2R from the centre i.e. is…..

Ans: 2

Explanation

We know that the electric field inside the sphere is given by

E=\frac{\rho_vr}{3\varepsilon} E(at\;r=R/2)=\frac{\rho_vR}{6\varepsilon}

Electric Field outside the sphere is given by,

E=\frac1{4\pi\varepsilon}\times\frac Q{r^2}=\frac{\rho_vR^3}{3\times\varepsilon\times r^2}…………as\;Q=\rho_v\frac43\pi R^3 E(at\;r=2R)=\frac{\rho_vR^3}{3\times\varepsilon\times4R^2}=\frac{\rho_vR}{12\varepsilon}

Taking ratio we can get the answer.

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