1. 0.44×10⁻¹³ C ² N ⁻¹ m ⁻² 2. 1.77×10⁻¹² C ² N ⁻¹ m ⁻² 3. 0.44×10⁻¹⁰ C ² N ⁻¹ m ⁻² 4. 5.00 C ² N ⁻¹ m ⁻²

Answer: 3. 0.44×10⁻¹⁰ C ² N ⁻¹ m ⁻² Capacitance with a dielectric of relative permittivity K is C=KC₀ . So K=30/6=5 Permittivity of the medium: ε=Kε₀=5×8.85×10⁻¹²=4.4×10⁻¹¹=0.44×10⁻¹⁰\ C²N⁻¹m⁻² Answer: option 3.

Topic: Capacitors, series and parallel combination, parallel plate capacitor with/without dielectric· Electrostatics

The capacitance of a parallel plate capacitor with air as medium is 6 μF. With the introduction of a dielectric medium, the capacitance becomes 30 μF. The permittivity of the medium is :(ε_0 = 8.85×10^-12 C^2 N^-1 m^-2)

1. $0.44\times10^{-13}$ C$^2$ N$^{-1}$ m$^{-2}$

2. $1.77\times10^{-12}$ C$^2$ N$^{-1}$ m$^{-2}$

3. $0.44\times10^{-10}$ C$^2$ N$^{-1}$ m$^{-2}$

4. 5.00 C$^2$ N$^{-1}$ m$^{-2}$

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Answer: 3. $0.44\times10^{-10}$ C$^2$ N$^{-1}$ m$^{-2}$

Capacitance with a dielectric of relative permittivity $K$ is $C=KC_0$. So

$$K=\frac{30}{6}=5$$

Permittivity of the medium:

$$\epsilon=K\epsilon_0=5\times8.85\times10^{-12}=4.4\times10^{-11}=0.44\times10^{-10}\ \text{C}^2\text{N}^{-1}\text{m}^{-2}$$

Answer: option 3.

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The capacitance of a parallel plate capacitor with air as medium is 6 μF. With the introduction of a dielectric medium, the capacitance becomes 30 μF. The permittivity of the medium is :(ε_0 = 8.85×10^-12 C^2 N^-1 m^-2)

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