Two charged conducting spheres S_1 and S_2 of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) When two conductors are connected by a wire, their potentials become equal $(V_1 = V_2)$.For a conducting sphere of radius $R$ and charge $q$, the

Vedclass · Accepted Answer

$\frac{9}{4}$

Vedclass · Answer

(D) When two conductors are connected by a wire, their potentials become equal $(V_1 = V_2)$.For a conducting sphere of radius $R$ and charge $q$, the potential is $V = \frac{kq}{R}$.Since the potentials are equal, we have $\frac{kq_1}{R_1} = \frac{kq_2}{R_2}$, which implies $\frac{q_1}{q_2} = \frac{R_1}{R_2}$.The electric field on the surface of a sphere is $E = \frac{kq}{R^2}$.Therefore, the ratio of the electric fields is $\frac{E_1}{E_2} = \frac{kq_1/R_1^2}{kq_2/R_2^2} = \frac{q_1}{q_2} \cdot \frac{R_2^2}{R_1^2}$.Substituting $\frac{q_1}{q_2} = \frac{R_1}{R_2}$ into the equation, we get $\frac{E_1}{E_2} = \frac{R_1}{R_2} \cdot \frac{R_2^2}{R_1^2} = \frac{R_2}{R_1}$.Given $R_1 = 8 	ext{ cm}$ and $R_2 = 18 	ext{ cm}$, the ratio is $\frac{E_1}{E_2} = \frac{18}{8} = \frac{9}{4}$.

Similar Questions

Two metal spheres $A$ and $B$ of radii $a$ and $b$ $(a < b)$ respectively are at a large distance apart. Each sphere carries a charge of $100 \mu C$. The spheres are connected by a conducting wire,then

The metal plate on the left in the figure carries a charge of $+q$. The metal plate on the right has a charge of $-2q$. What charge will flow through the switch $S$ when it is closed,if the central plate is initially neutral?

If two conducting spheres are separately charged and then brought in contact,which of the following statements is true?

$A$ charge $+q$ is placed somewhere inside the cavity of a thick conducting spherical shell of inner radius $R_1$ and outer radius $R_2$. $A$ charge $+Q$ is placed at a distance $r > R_2$ from the centre of the shell. Then the electric field in the hollow cavity

Two conducting spheres $A$ and $B$ have radii $1 \, mm$ and $2 \, mm$ respectively and are charged. They are placed at a distance of $5 \, cm$. When they are connected by a conducting wire,the ratio of the electric field intensities on their surfaces at equilibrium is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module