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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Capacitors

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Capacitors

For the arrangement of plates depicted in the figure, the...

For the arrangement of plates depicted in the figure, the capacitance between adjacent plates is 50 nF50 \text{ nF}. When a charge of 1.0μC1.0 \mu\text{C} is placed on the upper plate, what will be the potential difference between the upper plate and the middle plate?
For the arrangement of plates depicted in the figure, the capacitance between adjacent plates is 50 nF . When a charge

Options

  1. A10 V10 \text{ V}
  2. B0 V0 \text{ V}
  3. C5 V5 \text{ V}
  4. D20 V20 \text{ V}

Correct answer

A. 10 V10 \text{ V}

Step-by-step solution

Let the three parallel plates be denoted as 1 (upper), 2 (middle), and 3 (lower).

The total charges on the isolated plates are given as:
Q1=1.0μCQ_1 = 1.0 \mu\text{C}
Q2=0Q_2 = 0
Q3=0Q_3 = 0

For a system of parallel conducting plates, the charge appearing on the outermost surfaces is equal and is given by half the sum of the total charges on all plates:
qout=Q1+Q2+Q32=1.0μC+0+02=0.5μCq_{\text{out}} = \dfrac{Q_1 + Q_2 + Q_3}{2} = \dfrac{1.0 \mu\text{C} + 0 + 0}{2} = 0.5 \mu\text{C}

The charge on the upper surface of plate 1 is q1a=0.5μCq_{1a} = 0.5 \mu\text{C}.
The charge on the lower surface of plate 1 is q1b=Q1−q1a=1.0μC−0.5μC=0.5μCq_{1b} = Q_1 - q_{1a} = 1.0 \mu\text{C} - 0.5 \mu\text{C} = 0.5 \mu\text{C}.

The charge on the upper surface of plate 2 (facing plate 1) will be equal and opposite to q1bq_{1b}:
q2a=−q1b=−0.5μCq_{2a} = -q_{1b} = -0.5 \mu\text{C}

The upper and middle plates form a capacitor with charge q=0.5μCq = 0.5 \mu\text{C} on its inner surfaces.
Given the capacitance between adjacent plates is C=50 nFC = 50 \text{ nF}.

The potential difference VV between the upper and middle plates is:
V=qC=0.5×10−6 C50×10−9 F=500×10−950×10−9 V=10 VV = \dfrac{q}{C} = \dfrac{0.5 \times 10^{-6} \text{ C}}{50 \times 10^{-9} \text{ F}} = \dfrac{500 \times 10^{-9}}{50 \times 10^{-9}} \text{ V} = 10 \text{ V}
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