Question

Two conducting sphere of radii $$ r_1$$ and $$ r_2 $$ have same electric field near their surfaces. The ratio of their electrical potentials is

Answer 1

Correct option is C. $$ r_1/r_2 $$
$$ E_1=E_2 \Rightarrow \frac{kQ_1}{r_1^2}= \frac{kQ_2}{r_2^2} $$
$$ \frac { { Q }_{ 1 } }{ { Q }_{ 2 } } =\left( \frac { { r }_{ 1 } }{ { r }_{ 2 } } \right) ^{ 2 }$$
$$ \frac { { V }_{ 1 } }{ { V }_{ 2 } } =\frac { Q_{ 1 } }{ r_{ 1 } } \times \frac { { r }_{ 2 } }{ { Q }_{ 2 } } =\left( \frac { { r }_{ 1 } }{ { r }_{ 2 } } \right) ^{ 2 }\frac { { r }_{ 2 } }{ { r }_{ 1 } } =\frac { { r }_{ 1 } }{ { r }_{ 2 } } $$