A parallel plate capacitor is formed by two plates each of area 30$$\pi$$ cm² separated by 1 mm. A material of dielectric strength 3.6 $$\times$$ 10⁷ 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^$$-$$6C, the value of dielectric constant of the material is :

[Use $${1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9}$$ Nm² C^$$-$$2]

The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance $${r \over 2}$$ from the centre is :

Two metallic blocks M₁ and M₂ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M₂ is K then the thermal conductivity of M₁ will be :

[Assume steady state heat conduction]

0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127$$^\circ$$C. Th amount of heat required to double the speed of its molecules is ____________ k cal.

Take R = 2 cal mole^$$-$$1 K^$$-$$1)