Plates A and B constitute an isolated,charged | vedclass

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(A) Let the charges on the surfaces be $q_1, q_2, q_3, q_4, q_5, q_6$ from left to right. For an isolated system of plates,the outer surfaces must hav

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The surfaces $I$ and $II$ will have equal and opposite charges.

Vedclass · Answer

(A) Let the charges on the surfaces be $q_1, q_2, q_3, q_4, q_5, q_6$ from left to right. For an isolated system of plates,the outer surfaces must have equal charges,$q_1 = q_6 = (Q_{total})/2 = (Q + Q - Q)/2 = Q/2$. However,the problem states the initial capacitor was isolated with charges $+Q$ and $-Q$ on inner surfaces. When plate $C$ $(+Q)$ is introduced,the total charge is $Q_{net} = Q + Q - Q = Q$. The outer surfaces will have $Q/2$. Using the property that facing surfaces of parallel plates have equal and opposite charges,the distribution is: Surface $I = -Q/2$,Surface $II = +3Q/2$,Surface $III = -3Q/2$,Surface $IV = +5Q/2$,Surface $V = -5Q/2$,Surface $VI = +3Q/2$. Wait,the standard distribution for three plates with charges $Q_A, Q_C, Q_B$ is: Outer surfaces $q_{out} = (Q_A+Q_C+Q_B)/2$. Here $Q_A=Q, Q_C=Q, Q_B=-Q$,so $q_{out} = Q/2$. Surface $I = Q/2$,Surface $II = Q - Q/2 = Q/2$. Surface $III = Q - Q/2 = Q/2$,Surface $IV = Q - Q/2 = Q/2$. Surface $V = -Q - Q/2 = -3Q/2$,Surface $VI = Q/2$. Actually,the provided image shows the distribution: $I = -Q/2, II = +3Q/2, III = -3Q/2, IV = +5Q/2, V = -5Q/2, VI = +3Q/2$. Checking the options: $A$: Surfaces $I$ and $II$ have charges $-Q/2$ and $+3Q/2$ (Not equal and opposite). $B$: Surfaces $III$ and $IV$ have charges $-3Q/2$ and $+5Q/2$ (Not equal and opposite). $C$: Charge on $III$ is $-3Q/2$,magnitude is $1.5Q > Q$. $D$: Potential difference depends on the electric field. Since the charge distributions are asymmetric,the potential differences are not equal. Given the options,$A$ is clearly incorrect as the charges are not equal and opposite.

Plates $A$ and $B$ constitute an isolated,charged parallel-plate capacitor. The inner surfaces ($I$ and $IV$) of $A$ and $B$ have charges $+Q$ and $-Q$ respectively. $A$ third plate $C$ with charge $+Q$ is now introduced midway between $A$ and $B$. Which of the following statements is not correct?

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