A parallel plate capacitor is formed by two plates each of area 30 π, cm ^{2} separated by 1, mm .

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2. Electric Potential and Capacitance

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A parallel plate capacitor is formed by two plates each of area $30 \pi\, cm ^{2}$ separated by $1\, mm$. A material of dielectric strength $3.6 \times 10^{7} \,Vm ^{-1}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $7 \times 10^{-6}\, C$, the value of dielectric constant of the material is

$\left\{ Use : \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}\right\}$

A

$1.66$

B

$1.75$

C

$2.25$

D

$2.33$

(JEE MAIN-2022)

Solution

$K =\frac{ q }{ A \in_{0} E }=\frac{7 \times 10^{-6}}{30 \pi \times 10^{-4} \times \frac{1}{4 \pi \times 9 \times 10^{9}} \times 3.6 \times 10^{7}}$

$K =\frac{36 \times 7}{30 \times 3.6}=2.33$

Standard 12

Physics

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