For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is $${3 \over 4}$$d, where 'd' is the separation between the plates of parallel plate capacitor. The new capacitance (C') in terms of original capacitance (C₀) is given by the following relation :

A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time,
$$\overrightarrow B $$ = 8.0 $$\times$$ 10^$$-$$8 $$\widehat z$$T. The value of electric field at this point is :

(speed of light = 3 $$\times$$ 10⁸ ms^$$-$$1)

$$\widehat x$$, $$\widehat y$$, $$\widehat z$$ are unit vectors along x, y and z directions.

The maximum and minimum distances of a comet from the Sun are 1.6 $$\times$$ 10¹² m and 8.0 $$\times$$ 10¹⁰ m respectively. If the speed of the comet at the nearest point is 6 $$\times$$ 10⁴ ms^$$-$$1, the speed at the farthest point is :

A conducting wire of length 'l', area of cross-section A and electric resistivity $$\rho$$ is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current.

If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be :