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 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/)], where the time constant is equal to CR.)
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. \(1.2\times10^{-8} \hat{j}~\text{T}\)
1. | \( 2.16~\text{cm}, 24.1~\text{GHz} \) | 2. | \( 0.29~\text{cm}, 13.7~\text{GHz} \) |
3. | \( 3.23 ~\text{cm}, 20.0~\text{GHz} \) | 4. | \( 1.26~\text{cm}, 23.9~\text{GHz}\) |
1. | \(E_z=60 \sin \left(0.5 \times 10^3 x+1.5 \times 10^{11} t\right) ~\text{V/m} \) |
2. | \(E_z=60 \sin \left(1.5 \times 10^3 x+0.5 \times 10^{11} t\right) ~\text{V/m} \) |
3. | \(E_z=55 \sin \left(0.5 \times 10^3 x+1.5 \times 10^{11} t\right) ~\text{V/m} \) |
4. | \(E_z=55 \sin \left(1.5 \times 10^3 x+0.5 \times 10^{11} t\right) ~\text{V/m} \) |
Light with an energy flux of \(18~\text{W/cm}^{2}\) falls on a non-reflecting surface at normal incidence. If the surface has an area of \(20~\text{cm}^{2}\), what is the average force exerted on the surface during a \(30\) minute time span?
1. \(2.1\times10^{-6}~\text{N}\)
2. \(1.8\times10^{-6}~\text{N}\)
3. \(1.2\times10^{-6}~\text{N}\)
4. \(2.1\times10^{-5}~\text{N}\)
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 \(100~\text{W}\) bulb at a distance of \(3~\text{m}\) are respectively:
1. | \( 2.5 ~\text{V/m}, ~2.2 \times 10^{-8} ~\text{T} \) |
2. | \( 3.6 ~\text{V/m}, ~ 3.6 ~\text{T} \) |
3. | \( 4.07~\text{V/m},~ 1.4 \times 10^{-8} ~\text{T}\) |
4. | \( 4.2 ~\text{V/m}, ~3.4 \times 10^{-6}~\text{T}\) |