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

$A$ conducting sphere of radius $10 \ cm$ is charged with $10 \ \mu C$. Another uncharged sphere of radius $20 \ cm$ is brought into contact with it and then separated. The ratio of the surface charge densities on the spheres will be ....... (in $: 1$)

Consider a metal sphere of radius $R$ that is cut into two parts along a plane whose minimum distance from the sphere's centre is $h$. The sphere is uniformly charged with a total electric charge $Q$. The minimum force necessary to hold the two parts of the sphere together is:

Explain the construction of a Van de Graaff generator with a diagram and describe its uses.

$A$ solid spherical conducting shell has inner radius $a$ and outer radius $2a$. At the center of the shell, a point charge $+Q$ is located. What must the charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal?

Prove that,if an insulated,uncharged conductor is placed near a charged conductor and no other conductors are present,the uncharged body must be intermediate in potential between that of the charged body and that of infinity.

Vedclass Test Series

Exam Paper Generator

Online Exam Module