Capacitors

JEE Main level, single correct, medium

116 of 180

Question 116 of 180

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 :

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

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{{k\epsilon }_{0}\text{A}}{\text{d}}\cdot \text{E}\cdot \text{d}

=kϵ0AE=k{\epsilon }_{0}\text{AE}

QA=kϵ0E\dfrac{\text{Q}}{\text{A}}=k{\epsilon }_{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}

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