Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $$\pi / 2$$ and $$\pi / 3$$ at points $$\mathrm{A}$$ and $$\mathrm{B}$$ respectively. The difference between the resultant intensities at the two points is $$x I$$. The value of $$x$$ will be ________.

To light, a $$50 \mathrm{~W}, 100 \mathrm{~V}$$ lamp is connected, in series with a capacitor of capacitance $$\frac{50}{\pi \sqrt{x}} \mu F$$, with $$200 \mathrm{~V}, 50 \mathrm{~Hz} \,\mathrm{AC}$$ source. The value of $$x$$ will be ___________.

A $$1 \mathrm{~m}$$ long copper wire carries a current of $$1 \mathrm{~A}$$. If the cross section of the wire is $$2.0 \mathrm{~mm}^{2}$$ and the resistivity of copper is $$1.7 \times 10^{-8}\, \Omega \mathrm{m}$$, the force experienced by moving electron in the wire is ____________ $$\times 10^{-23} \mathrm{~N}$$.

(charge on electorn $$=1.6 \times 10^{-19} \,\mathrm{C}$$)

A long cylindrical volume contains a uniformly distributed charge of density $$\rho \,\mathrm{Cm}^{-3}$$. The electric field inside the cylindrical volume at a distance $$x=\frac{2 \varepsilon_{0}}{\rho} \mathrm{m}$$ from its axis is ________ $$\mathrm{Vm}^{-1}$$.