question_answer

A spherical shell of radius 10 cm is carrying a charge q. If the electric potential at distances .5 cm, 10 cm and 15 cm from the center of the spherical shell is Vi, V. and V^ respectively, then

A)  \[{{V}_{1}}<{{V}_{2}}<{{V}_{3}}\]

B)  \[{{V}_{1}}={{V}_{2}}<{{V}_{3}}\]

C)  \[{{V}_{1}}>{{V}_{2}}>{{V}_{3}}\]

D)  \[{{V}_{1}}={{V}_{2}}>{{V}_{3}}\]

Correct Answer: D

Solution :

 :As \[{{V}_{inside}}={{V}_{surface}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{R}\] and \[{{V}_{outside}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{r}\] where q is the charge on the shell and R its radius. \[\therefore \] \[{{V}_{1}}={{V}_{2}}>{{V}_{3}}\]