Displacement current exists within the gap between the plates of capacitor when the electric field between its plates
Displacement current is given by \(I_d = \varepsilon_0 \frac{d\Phi_E}{dt}\). It exists whenever there is a changing electric field, whether it increases or decreases with time.
Speed of EM wave in free space is given by (where symbols have their usual meaning)
From Maxwell's electromagnetic theory, the speed of light \( c \) in vacuum is determined by the electric permittivity \( \varepsilon_0 \) and magnetic permeability \( \mu_0 \) of free space through the relation \( c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \).
Displacement current exists within the gap between the plates of capacitor when the electric field between its plates
Displacement current is given by \(I_d = \varepsilon_0 \frac{d\Phi_E}{dt}\). Hence, it exists whenever the electric field changes (increases or decreases) with time.
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): Conduction and displacement current may be present in the same region of space.
Reason (R): There is no perfectly conducting or perfectly insulating medium.
In a real dielectric medium with some conductivity, both conduction current (due to charge movement) and displacement current (due to changing electric fields) can exist simultaneously. As no material is perfectly conducting or insulating, this coexistence is possible.
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.