Question 1:
easyTo produce an instantaneous displacement current of 2 mA in the space between the parallel plates of a capacitor of capacitance 4 \(\mu\)F, the rate of change of applied variable potential difference \(\left(\frac{dV}{dt}\right)\) must be
Displacement current is given by \(I_d = C \frac{dV}{dt}\). Substituting the values: \(2 \times 10^{-3} = 4 \times 10^{-6} \frac{dV}{dt} ⇒ \frac{dV}{dt} = 500\text{ V/s}\).
Question 2:
easyIn an electromagnetic wave, (travelling in vacuum) \(E = 1.2 \sin(2 \times 10^6 t – kx)\text{ N/C}\). Find the value of maximum intensity of magnetic field:
Maximum magnetic field \(B_0 = \frac{E_0}{c} = \frac{1.2}{3 \times 10^8} = 4 \times 10^{-9}\text{ T}\). The intensity of magnetic field is \(H_0 = \frac{B_0}{\mu_0} = \frac{4 \times 10^{-9}}{4\pi \times 10^{-7}} = \frac{10^{-2}}{\pi}\text{ A/m}\).
Question 3:
easyDisplacement current is same as:
Displacement current represents the rate of change of electric displacement field and is not caused by real movement of charges like conduction current.
Question 4:
easyThe potential difference between the plates of a parallel plate capacitor is changing at the rate of \(10^6\text{ V/s}\). If the capacitance is \(2\ \mu\text{F}\), the displacement current in the dielectric of the capacitor will be:
Displacement current is given by \(I_d = C \frac{dV}{dt}\). Substituting \(C = 2 \times 10^{-6}\text{ F}\) and \(\frac{dV}{dt} = 10^6\text{ V/s}\), we find \(I_d = 2\text{ A}\).
Question 5:
easyModified ampere circuital law is given by (symbols have their usual meaning)
The generalized Ampere's circuital law (or Ampere-Maxwell law) includes both conduction current \(I_C\) and displacement current \(I_D\) as sources of magnetic fields, expressed as \(\oint \vec{B} \cdot d\vec{l} = \mu_0(I_C + I_D)\).
Question 6:
easyA capacitor of capacitance \(C\), is connected across an ac source of voltage \(V\), given by \(V = V_0\sin\omega t\). The displacement current between the plates of the capacitor, would then be given by
The displacement current is equal to the conduction current, which is \(I_d = \frac{dq}{dt}\). Since \(q = CV = C V_0 \sin\omega t\), differentiating with respect to time gives \(I_d = V_0 \omega C \cos\omega t\).
Question 7:
easyFor a plane electromagnetic wave propagating in \(x\)-direction, which one of the following combination gives the correct possible directions for electric field (\(vec{E}\)) and magnetic field (\(vec{B}\)) respectively?
The direction of propagation of an electromagnetic wave is given by the cross product \(vec{E} \times \vec{B}\). For wave propagation along the positive \(x\)-direction, the cross product must yield a positive \(hat{i}\) vector. Using option C, \((-\hat{j} + \hat{k}) \times (-\hat{j} - \hat{k}) = \hat{j}\times\hat{k} - \hat{k}\times\hat{j} = 2\hat{i}\), which satisfies this condition.
Question 8:
easyMatch List-I with List-II.
List-I (Types of EM waves)
a. Infrared rays
b. Microwaves
c. UV rays
d. Gamma rays
List-II (Application)
(i) Water purifier
(ii) Remote switches
(iii) Used in medicine to destroy cancer cells
(iv) Cooking
Choose the correct option:
Infrared is used in remote switches (a-ii); Microwaves for cooking (b-iv); UV rays for water purification (c-i); and Gamma rays in cancer cell destruction (d-iii).
Question 9:
easyMatch column I with column II.
| Column-I (Types of EM waves) | Column-II (Production) |
| A. Infra-red | P. Rapid vibration of electrons in aerials |
| B. Radio | Q. Electrons in atoms emit light when they move from higher to lower energy level. |
| C. Light | R. Klystron valve |
| D. Microwave | S. Vibration of atoms and molecules |
Choose the correct match from the options given below:
Infrared waves are produced by molecular vibrations (A-S). Radio waves by accelerating charges in aerials (B-P). Light waves by atomic transitions (C-Q). Microwaves by klystron/magnetron valves (D-R).
Question 10:
easyFor a plane EM wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (\(\vec{E}\) ) and magnetic field (\(\vec{B}\) ) respectively?
The direction of propagation of an electromagnetic wave is along \(\vec{E} \times \vec{B}\). Here, \((-\hat{j} + \hat{k}) \times (-\hat{j} - \hat{k}) = 2\hat{i}\), which points in the positive x-direction.