**Assertion (A):** When electromagnetic waves are incident on a surface, exert radiation pressure on the surface.
**Reason (R):** Electromagnetic waves carry energy as well as momentum.
EM waves carry momentum. When they strike a surface, their momentum changes, exerting a force and thus pressure. Therefore, Assertion and Reason are true, and R is the correct explanation for A.
**Assertion (A):** In an electromagnetic wave, both the electric and magnetic field vibrates with same phase and frequency.
**Reason (R):** Amplitude of vibration of electric and magnetic field are equal in an electromagnetic wave.
In an EM wave, electric and magnetic fields oscillate in phase and with the same frequency. However, their amplitudes are related by \(E_0 = cB_0\) and are generally not equal. Thus, A is true, but R is false.
**Assertion (A):** The energy in a small volume through which an EM wave is passing oscillates with double the frequency of wave.
**Reason (R):** The electric field and magnetic field can not have equal average numerical value in each half cycle.
The energy density of an EM wave involves \(E^2\) and \(B^2\), which oscillate at \(2omega\). So, A is true. The average magnitudes of \(E\) and \(B\) over a half-cycle are not equal because \(E_0 = cB_0\). So, R is true. However, R does not explain A.
Assertion (A): A magnetic needle when placed in between the plates of a parallel plate capacitor under charging, the needle shows deflection.
Reason (R):As the charge on the capacitor plates increases, the electric field and the electric flux between the plates changes which generates a magnetic field.
During capacitor charging, the changing electric field produces a displacement current \(I_d = epsilon_0 frac{dPhi_E}{dt}\). This displacement current generates a magnetic field, causing the needle to deflect. Thus, A and R are true, and R explains A.
Assertion (A): In an electromagnetic wave, magnitude of magnetic field vector is much smaller than the magnitude of electric field vector.
Reason (R): Energy of electromagnetic waves is shared equally by the electric and magnetic fields.
In an EM wave, \(E_0 = cB_0\). Since \(c = 3 times 10^8 text{ m/s}\), \(E_0\) is much larger than \(B_0\) in SI units, so A is true. Energy is equally shared between fields, so R is true. However, R does not explain why \(E_0\) is numerically larger than \(B_0\).
**Assertion (A):** The gyrating electron can be a source of EMW.
**Reason (R):** The electron in circular motion is accelerated motion.
A gyrating electron undergoes circular motion, which is accelerated motion. Accelerated charges are sources of electromagnetic waves. Therefore, Assertion and Reason are true, and R correctly explains A.
\(\varepsilon_0\) and \(\mu_0\) are the electric permittivity and magnetic permeability of free space respectively. If the corresponding quantities of a medium are \(2\varepsilon_0\) and \(1.5\mu_0\) respectively, the refractive index of the medium will nearly be
The refractive index is given by \(n = \frac{c}{v} = \sqrt{\frac{\varepsilon \mu}{\varepsilon_0 \mu_0}} = \sqrt{2 times 1.5} = \sqrt{3}\).
To produce an instantaneous displacement current of 2 mA in the space between the parallel plates of a capacitor of capacitance \(4 \mu\text{F}\), the rate of change of applied variable potential difference \(\left(\frac{dV}{dt}\right)\) must be
Since displacement current is given by \(I_d = C \frac{dV}{dt}\), we find \(\frac{dV}{dt} = \frac{I_d}{C} = \frac{2 \times 10^{-3} \text{A}}{4 \times 10^{-6} \text{F}} = 500 \text{V/s}\).
Part of EM spectrum which is used to destroy bacteria and sterilizing the surgical instruments is
Ultraviolet (UV) rays are widely used for germicidal and sterilization applications because their energy is sufficient to disrupt bacterial DNA.
The velocity of an electromagnetic wave is along (where E represents the electric field and B represents the magnetic field)
The direction of propagation of an electromagnetic wave is given by Poynting vector, which is parallel to the cross product of electric and magnetic fields, \(\vec{E} \times \vec{B}\).