Standard air filled rectangular waveguides of dimensions a = 2.29cm and b = 1.02cm are designed for radar applications. It is desired that these waveguides operate only in the dominant $$T{E_{10}}$$ mode with the operating frequency at least 25% above the cut-off frequency of the $$T{E_{10}}$$ mode but not higher than 95% of the next higher cutoff frequency. The range of the allowable operating frequency f is

The permittivity of water at optical frequencies is $$1.75{\varepsilon _0}$$. It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius $$5m$$, as shown in the figure. The critical angle is $${\theta _c}$$

The value of $$d$$ (in meter) is ______ .

Two conducting spheres S1 and S2 of radii a and b (b>a) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure.

For some charge placed on this structure, the potential and surface electric field on S1 are V_a and E_a , and that on S2 are V_b and E_b, respectively, which of the following is CORRECT?

An electron (q₁) is moving in free space with velocity 10⁵ m/s towards a stationary electron (q₂) far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is ___________ ×10^-8m.

[Given, mass of electron m = 9.11×10^-31 kg, charge of electron e = -1.6×10^-19 C , and permittivity $$\varepsilon_0=\left(1/36\mathrm\pi\right)\times10^{-9}\;\mathrm F/\mathrm m$$].