Question

An EM wave from air enters a medium. The electric fields are $$\overrightarrow {{E_1}} = {E_{01}}\hat x\cos \left[ {2\pi v\left( {\frac{z}{c} - t} \right)} \right]$$      in air and $$\overrightarrow {{E_2}} = {E_{02}}\hat x\cos \left[ {k\left( {2z - ct} \right)} \right]$$      in medium, where the wave number $$k$$ and frequency $$v$$ refer to their values in air. The medium is nonmagnetic. If $${ \in _{{r_1}}}$$ and $${ \in _{{r_2}}}$$ refer to relative permittivities of air and medium respectively, which of the following options is correct?

A. $$\frac{{{ \in _{{r_1}}}}}{{{ \in _{{r_2}}}}} = 4$$
B. $$\frac{{{ \in _{{r_1}}}}}{{{ \in _{{r_2}}}}} = 2$$
C. $$\frac{{{ \in _{{r_1}}}}}{{{ \in _{{r_2}}}}} = \frac{1}{4}$$  
D. $$\frac{{{ \in _{{r_1}}}}}{{{ \in _{{r_2}}}}} = \frac{1}{2}$$
Answer :   $$\frac{{{ \in _{{r_1}}}}}{{{ \in _{{r_2}}}}} = \frac{1}{4}$$
Solution :
Velocity of EM wave is given by $$v = \frac{1}{{\sqrt {\mu \in } }}$$
Velocity in air = $$\frac{\omega }{k} = C$$
Velocity in medium = $$\frac{C}{2}$$
Here, $${\mu _1} = {\mu _2} = 1$$   as medium is non-magnetic
$$\therefore \frac{{\frac{1}{{\sqrt {{ \in _{{r_1}}}} }}}}{{\frac{1}{{\sqrt {{ \in _{{r_2}}}} }}}} = \frac{C}{{\left( {\frac{C}{2}} \right)}} = 2 \Rightarrow \frac{{{ \in _{{r_1}}}}}{{{ \in _{{r_2}}}}} = \frac{1}{4}$$

Releted MCQ Question on
Electrostatics and Magnetism >> Electromagnetic Induction

Releted Question 1

A thin circular ring of area $$A$$ is held perpendicular to a uniform magnetic field of induction $$B.$$ $$A$$ small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is $$R.$$ When the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is

A. $$\frac{{BR}}{A}$$
B. $$\frac{{AB}}{R}$$
C. $$ABR$$
D. $$\frac{{{B^2}A}}{{{R^2}}}$$
Releted Question 2

A thin semi-circular conducting ring of radius $$R$$ is falling with its plane vertical in horizontal magnetic induction $$\overrightarrow B .$$  At the position $$MNQ$$  the speed of the ring is $$v,$$ and the potential difference developed across the ring is
Electromagnetic Induction mcq question image

A. zero
B. $$\frac{{Bv\pi {R^2}}}{2}$$  and $$M$$ is at higher potential
C. $$\pi RBv$$  and $$Q$$ is at higher potential
D. $$2RBv$$  and $$Q$$ is at higher potential
Releted Question 3

Two identical circular loops of metal wire are lying on a table without touching each other. Loop-$$A$$ carries a current which increases with time. In response, the loop-$$B$$

A. remains stationary
B. is attracted by the loop-$$A$$
C. is repelled by the loop-$$A$$
D. rotates about its $$CM,$$  with $$CM$$  fixed
Releted Question 4

A coil of inductance $$8.4 mH$$  and resistance $$6\,\Omega $$  is connected to a $$12 V$$  battery. The current in the coil is $$1.0 A$$  at approximately the time

A. $$500 s$$
B. $$25 s$$
C. $$35 ms$$
D. $$1 ms$$

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Electromagnetic Induction


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