Consider two charged metallic spheres S_{1} a | vedclass

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

Question

(D) The electric field on the surface of a charged sphere is given by $E = \frac{KQ}{R^{2}}.$Given $E_{1} = \frac{KQ_{1}}{R_{1}^{2}}$ and $E_{2} = \fr

Vedclass · Accepted Answer

$(R_{1} / R_{2})^{2}$

Vedclass · Answer

(D) The electric field on the surface of a charged sphere is given by $E = \frac{KQ}{R^{2}}.$Given $E_{1} = \frac{KQ_{1}}{R_{1}^{2}}$ and $E_{2} = \frac{KQ_{2}}{R_{2}^{2}}.$According to the problem,$\frac{E_{1}}{E_{2}} = \frac{R_{1}}{R_{2}}.$Substituting the expressions,we get $\frac{KQ_{1} / R_{1}^{2}}{KQ_{2} / R_{2}^{2}} = \frac{R_{1}}{R_{2}}.$$\frac{Q_{1}}{Q_{2}} \cdot \frac{R_{2}^{2}}{R_{1}^{2}} = \frac{R_{1}}{R_{2}} \implies \frac{Q_{1}}{Q_{2}} = \frac{R_{1}^{3}}{R_{2}^{3}}.$The electrostatic potential on the surface of a sphere is $V = \frac{KQ}{R}.$Therefore,$\frac{V_{1}}{V_{2}} = \frac{KQ_{1} / R_{1}}{KQ_{2} / R_{2}} = \frac{Q_{1}}{Q_{2}} \cdot \frac{R_{2}}{R_{1}}.$Substituting $\frac{Q_{1}}{Q_{2}} = \frac{R_{1}^{3}}{R_{2}^{3}},$ we get $\frac{V_{1}}{V_{2}} = \frac{R_{1}^{3}}{R_{2}^{3}} \cdot \frac{R_{2}}{R_{1}} = \frac{R_{1}^{2}}{R_{2}^{2}} = (R_{1} / R_{2})^{2}.$

$List-I$	$List-II$
$(P)$ The capacitance between $S_1$ and $S_4$, with $S_2$ and $S_3$ not connected, is	$(1)$ $3 C_0$
$(Q)$ The capacitance between $S_1$ and $S_4$, with $S_2$ shorted to $S_3$, is	$(2)$ $C_0 / 2$
$(R)$ The capacitance between $S_1$ and $S_3$, with $S_2$ shorted to $S_4$, is	$(3)$ $C_0 / 3$
$(S)$ The capacitance between $S_1$ and $S_2$, with $S_3$ shorted to $S_1$, and $S_2$ shorted to $S_4$, is	$(4)$ $2 C_0 / 3$
	$(5)$ $2 C_0$

Similar Questions

$A$ parallel plate capacitor is charged fully by using a battery. Then,without disconnecting the battery,the plates are moved further apart. Then,

Three capacitors $C_{1} = 2 \, \mu F$,$C_{2} = 6 \, \mu F$,and $C_{3} = 12 \, \mu F$ are connected as shown in the figure. Find the ratio of the charges on capacitors $C_{1}$,$C_{2}$,and $C_{3}$ respectively.

When a soap bubble is charged,its size:

Vedclass Test Series

Exam Paper Generator

Online Exam Module