Assertion (A): When cooking in microwave ovens, metal containers are used.
Reason (R): Energy of microwaves can be easily transferred to the food through metal.
Metal containers reflect microwaves and are not used in microwave ovens. Microwaves heat food by interacting with water molecules, not through metal. Thus, both assertion and reason are false.
Assertion (A): Infrared waves are often called heat waves.
Reason (R): Infrared waves vibrate not only electrons but entire atoms or molecules.
Infrared waves are absorbed by molecules, increasing their vibrational and rotational energy, which manifests as heat. Thus, both A and R are true, and R explains A.
Assertion (A): Electromagnetic waves cannot penetrate through a perfect conductor and hence are totally reflected.
Reason (R): The speed of electromagnetic waves in any dielectric medium is less as compared to vacuum.
A perfect conductor contains free charges that rapidly reorient to cancel the incident electric field, causing total reflection. The speed of EM waves in a dielectric is slower than in vacuum due to the interaction with the medium's polarization. Both statements are true, but R does not explain A.
Assertion (A): Electromagnetic radiations like UV, visible and IR coming from Sun towards earth’s surface can’t be trapped by earth’s magnetic field where as cosmic rays coming towards earth’s surface are trapped by the magnetic field of earth.
Reason (R): Electromagnetic wave doesn’t contain any live charge where the cosmic rays is a huge storage of charged particle.
Electromagnetic waves consist of photons and carry no charge, hence they are unaffected by magnetic fields. Cosmic rays are composed of charged particles, which experience a Lorentz force in the Earth's magnetic field, causing them to be trapped or deflected. Thus, R correctly explains A.
Assertion (A): An E.M. wave has constantly interchanging electric and magnetic fields, which are perpendicular to each other.
Reason (R): The direction of propagation is given by \((\vec{B} \times \vec{E})\).
Electromagnetic waves consist of perpendicular oscillating electric and magnetic fields. The direction of propagation is given by \((\vec{E} \times \vec{B})\) (Poynting vector), not \((\vec{B} \times \vec{E})\). Thus, A is true, but R is false.
Assertion (A): Average value of electric field and magnetic field in one cycle is same in electromagnetic waves.
Reason (R): The ratio of electric field intensity and magnetic field intensity of EM waves is equal to speed of EM waves.
In electromagnetic waves, the average energy density stored in the electric field is equal to the average energy density stored in the magnetic field over one cycle. Also, the ratio of electric field intensity to magnetic field intensity equals the wave's speed \(v\). Both statements are true, but the second does not explain the first.
**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): 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 \(B_0\).