A parallel plate capacitor with circular plates of radius 1 m has a capacitance of 1 nF. At t = 0, it is connected for charging in series with a resistor R = 1 M$\Omega$ across a 2V battery (as shown in the figure). Find the magnetic field at a point P, halfway between the centre and the periphery of the plates, after t = 10^–3 s. (The charge on the capacitor at time t is q (t) = CV[1 – exp (–t/$\tau$)], where the time constant $\tau$ is equal to CR.) 

$1. 0.74\times {10}^{-13} T$
$2. 0.67\times {10}^{-13} T$
$3. 0.74\times {10}^{-12} T$
$4. 0.67\times {10}^{-12} T$

A plane electromagnetic wave of frequency 25 MHz travels in free space along the x-direction. At a particular point in space and time, $$\(\vec{E_{0}}=6.3~ \hat{j}~V/m\). What is \(\vec{B_{0}}\) at this point?
1. \(2.1\times 10^{-8} \hat{k}~\text{T}\)
2. \(1.2\times10^{-8} \hat{k}~\text{T}\)
3. \(2.1\times10^{-8} \hat{j}~\text{T}\)
4. \(1.2\times10^{-8} \hat{j}~\text{T}\)$\mathrm{}$

The magnetic field in a plane electromagnetic wave is given by \(\mathrm{B}=\left(2 \times 10^{-7}\right) \mathrm{T} \sin \left(0.5 \times 10^3 \mathrm{x}+1.5 \times 10^{11} \mathrm{t}\right )\). The wavelength and frequency of the wave are respectively:

The magnetic field in a plane electromagnetic wave is given by \(\mathrm{B}=\left(2 \times 10^{-7}\right) \mathrm{T} \sin \left(0.5 \times 10^3 \mathrm{x}+1.5 \times 10^{11} \mathrm{t}\right)\). The expression for the electric field is:
1. \( \mathrm{E}_{\mathrm{z}}=60 \sin \left(0.5 \times 10^3 \mathrm{x}+1.5 \times 10^{11} \mathrm{t}\right) \mathrm{V} / \mathrm{m} \)
2. \( \mathrm{E}_{\mathrm{z}}=60 \sin \left(1.5 \times 10^3 \mathrm{x}+0.5 \times 10^{11} \mathrm{t}\right) \mathrm{V} / \mathrm{m} \)
3. \( \mathrm{E}_{\mathrm{z}}=55 \sin \left(0.5 \times 10^3 \mathrm{x}+1.5 \times 10^{11} \mathrm{t}\right) \mathrm{V} / \mathrm{m} \)
4. \( \mathrm{E}_{\mathrm{z}}=55 \sin \left(1.5 \times 10^3 \mathrm{x}+0.5 \times 10^{11} \mathrm{t}\right) \mathrm{V} / \mathrm{m}\)$\mathrm{}$

Light with an energy flux of 18 W/cm² falls on a non-reflecting surface at normal incidence. If the surface has an area of 20 cm², what is the average force exerted on the surface during a 30 minute time span?

$1. 2.1\times {10}^{-6} \mathrm{N}$
$2. 1.8\times {10}^{-6} \mathrm{N}$
$3. 1.2\times {10}^{-6} \mathrm{N}$
$4. 2.1\times {10}^{-5} \mathrm{N}$

Assume a bulb of efficiency \(2.5\%\) as a point source. The peak values of the electric field and magnetic field produced by the radiation coming from a \(100~\mathrm{W}\) bulb at a distance of \(3~\mathrm{m}\) are respectively: