An electric field, $$\overrightarrow{\mathrm{E}}=\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}}$$ passes through the surface of $$4 \mathrm{~m}^2$$ area having unit vector $$\hat{n}=\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$$. The electric flux for that surface is _________ $$\mathrm{Vm}$$.
Two open organ pipes of lengths $$60 \mathrm{~cm}$$ and $$90 \mathrm{~cm}$$ resonate at $$6^{\text {th }}$$ and $$5^{\text {th }}$$ harmonics respectively. The difference of frequencies for the given modes is _________ $$\mathrm{Hz}$$. (Velocity of sound in air $$=333 \mathrm{~m} / \mathrm{s}$$)
Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $$P$$ is $$\frac{x \sigma}{\epsilon_0}$$. The value of $$x$$ is _________ (all quantities are measured in SI units).
The electric field at point $$\mathrm{p}$$ due to an electric dipole is $$\mathrm{E}$$. The electric field at point $$\mathrm{R}$$ on equitorial line will be $$\frac{\mathrm{E}}{x}$$. The value of $$x$$ :