Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20146 April
Exam
JEE Main
Year
2014
Date
6 April
Subject
Physics
Chapter
Capacitance

JEE Main 2014 · 6 April · Physics · Capacitance

A parallel plate capacitor is made of two circular plates separated...

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3×104V/m3 \times 1 {0}^{4} \text{V/m}, the charge density of the positive plate will be close to :

Options

  1. A6×10−7C/m26 \times 1 {0}^{- 7} \text{C} / {\text{m}}^{2}
  2. B3×10−7C/m23 × 1 {0}^{- 7} \text{C} / {\text{m}}^{2}
  3. C3×104C/m23 × 1 {0}^{4} \text{C} / {\text{m}}^{2}
  4. D6×104C/m26 × 1 {0}^{4} \text{C} / {\text{m}}^{2}

Correct answer

A. 6×10−7C/m26 \times 1 {0}^{- 7} \text{C} / {\text{m}}^{2}

Step-by-step solution

E=3×104V/m\text{E} = 3 \times 1 {0}^{4} \text{V/m}

We know that

Q=CV\text{Q} = \text{CV}

=kε0Ad⋅E⋅d= \dfrac{{kε}_{0}\text{A}}{\text{d}} \cdot \text{E} \cdot \text{d}

=kε0AE= k{ε}_{0}\text{AE}

QA=kε0E\dfrac{\text{Q}}{\text{A}} = k{ε}_{0}\text{E}

=2.2×8.85×10−12×3×104= 2.2 \times 8.85 \times {10}^{- 12} \times 3 \times {10}^{4}

=58.41×10−8= 58.41 \times {10}^{- 8}

=5.84×10−7= 5.84 \times {10}^{- 7}

≈6×10−7C/m2\approx 6 \times {10}^{- 7}C / {m}^{2}
Practice Capacitance on Quantrex Academy →

More from Capacitance

Passage: A container of height 2 m, length 2 m and breadth 1 m is made of insulating… JEE Advanced 2026A parallel plate capacitor is having separation between plates 0.885 mm. It has a… JEE Main 2026A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical… JEE Main 2026From the circuit given below, the capacitance between terminals A and B shown in the… JEE Main 2026A parallel plate air capacitor is connected to a battery. The plates are pulled apart at… JEE Main 2026Consider a circuit consisting of a capacitor ( 20\ μ F), resistor ( 100\ Ω ) and two… JEE Main 2026The dimensional formula of (1)/(2)ε_0 E^2 ( ε_0 = permittivity of vacuum and E = electric… JEE Main 2026A parallel plate air capacitor has a capacitance C . When it is half filled as show in… JEE Main 2026 Full Capacitance list All JEE Main PYQs