#### Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres A and B is  Option 1) Option 2) Option 3) Option 4)

As we learnt in

Electric Field Intensity -

- wherein

Capacitance of Conductor -

- wherein

C - Capacity or capacitance of conductor

V - Potential.

When the spherical conductors are connected by a conducting wire, charge is redistributed and the spheres attain a common potentia  V.

$\therefore\: \: \: Intensity \: E_{A}= \frac{1}{4\pi \varepsilon _{0}}\frac{Q_{A}}{R_{A}^{2}}$

$or\: \: \: \: E_{A}= \frac{1\times C_{A}V}{4\pi \varepsilon _{0}R_{A}^{2}}= \frac{\left ( 4\pi \varepsilon _{0}R_{A} \right )V}{4\pi \varepsilon _{0}R_{A}^{2}}= \frac{V}{R_{A}}$

Similarly  $E_{B}= \frac{V}{R_{B}}$

$\therefore \frac{E_{A}}{E_{B}}= \frac{R_{B}}{R_{A}}= \frac{2}{1}$

Option 1)

Incorrect

Option 2)

Incorrect

Option 3)

Incorrect

Option 4)

Correct