Electromagnetic Waves
PHXI15:WAVES

358955 The electric field of an electromagnetic wave in free space is given by:
\({E=10 \cos \left(10^{7} t+k x\right) V / m}\)
where \({t}\) and \({x}\) are in seconds and metres, respectively. It can be inferred that
(a) the wavelength \({\lambda}\) is \(188.4\,m\)
(b) the wave number \({k}\) is \(0.33\,rad/m\)
(c) the wave amplitude is \(10\,V/m\)
(d) the wave is propagating along \({+x}\)-direction.
Which one of the following pairs of statements is correct?

1 (a) and (b)
2 (b) and (c)
3 (a) and (c)
4 (c) and (d)
PHXI15:WAVES

358956 Assertion :
Accelerated charge radiate electromagnetic waves.
Reason :
Oscillating electric and magnetic fields regenerate each other.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

358957 If the magnetic field in a plane electromagnetic wave is given by
\(\vec{B}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{j} T\), then what will be expression for electric field?

1 \(\vec{E}=\left[9 \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{k} V / m\right]\)
2 \(\vec{E}=\left[60 \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{k} V / m\right]\)
3 \(\vec E = \left[ {3 \times {{10}^{ - 8}}\sin \left( {1.6 \times {{10}^3}x + 48 \times {{10}^{10}}t} \right)\hat i\;V/m} \right]\)
4 \(\vec E = \left[ {3 \times {{10}^{ - 8}}\sin \left( {1.6 \times {{10}^3}x + 48 \times {{10}^{10}}t} \right)\hat j\;V/m} \right]\)
PHXI15:WAVES

358958 Magnetic field in plane electromagnetic wave is given by \(\vec{B}=B_{0} \sin (k x+\omega t) \hat{j} T\). Expression for corresponding electric field will be

1 \(\vec{E}=-B_{0} c \sin (k x+\omega t) \hat{k} V / m\)
2 \(\vec{E}=B_{0} c \sin (k x-\omega t) \hat{k} V / m\)
3 \(\vec{E}=B_{0} c \sin (k x+\omega t) \hat{k} V / m\)
4 \(\vec{E}=\dfrac{B_{0}}{c} \sin (k x+\omega t) \hat{k} V / m\)
PHXI15:WAVES

358955 The electric field of an electromagnetic wave in free space is given by:
\({E=10 \cos \left(10^{7} t+k x\right) V / m}\)
where \({t}\) and \({x}\) are in seconds and metres, respectively. It can be inferred that
(a) the wavelength \({\lambda}\) is \(188.4\,m\)
(b) the wave number \({k}\) is \(0.33\,rad/m\)
(c) the wave amplitude is \(10\,V/m\)
(d) the wave is propagating along \({+x}\)-direction.
Which one of the following pairs of statements is correct?

1 (a) and (b)
2 (b) and (c)
3 (a) and (c)
4 (c) and (d)
PHXI15:WAVES

358956 Assertion :
Accelerated charge radiate electromagnetic waves.
Reason :
Oscillating electric and magnetic fields regenerate each other.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

358957 If the magnetic field in a plane electromagnetic wave is given by
\(\vec{B}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{j} T\), then what will be expression for electric field?

1 \(\vec{E}=\left[9 \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{k} V / m\right]\)
2 \(\vec{E}=\left[60 \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{k} V / m\right]\)
3 \(\vec E = \left[ {3 \times {{10}^{ - 8}}\sin \left( {1.6 \times {{10}^3}x + 48 \times {{10}^{10}}t} \right)\hat i\;V/m} \right]\)
4 \(\vec E = \left[ {3 \times {{10}^{ - 8}}\sin \left( {1.6 \times {{10}^3}x + 48 \times {{10}^{10}}t} \right)\hat j\;V/m} \right]\)
PHXI15:WAVES

358958 Magnetic field in plane electromagnetic wave is given by \(\vec{B}=B_{0} \sin (k x+\omega t) \hat{j} T\). Expression for corresponding electric field will be

1 \(\vec{E}=-B_{0} c \sin (k x+\omega t) \hat{k} V / m\)
2 \(\vec{E}=B_{0} c \sin (k x-\omega t) \hat{k} V / m\)
3 \(\vec{E}=B_{0} c \sin (k x+\omega t) \hat{k} V / m\)
4 \(\vec{E}=\dfrac{B_{0}}{c} \sin (k x+\omega t) \hat{k} V / m\)
PHXI15:WAVES

358955 The electric field of an electromagnetic wave in free space is given by:
\({E=10 \cos \left(10^{7} t+k x\right) V / m}\)
where \({t}\) and \({x}\) are in seconds and metres, respectively. It can be inferred that
(a) the wavelength \({\lambda}\) is \(188.4\,m\)
(b) the wave number \({k}\) is \(0.33\,rad/m\)
(c) the wave amplitude is \(10\,V/m\)
(d) the wave is propagating along \({+x}\)-direction.
Which one of the following pairs of statements is correct?

1 (a) and (b)
2 (b) and (c)
3 (a) and (c)
4 (c) and (d)
PHXI15:WAVES

358956 Assertion :
Accelerated charge radiate electromagnetic waves.
Reason :
Oscillating electric and magnetic fields regenerate each other.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

358957 If the magnetic field in a plane electromagnetic wave is given by
\(\vec{B}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{j} T\), then what will be expression for electric field?

1 \(\vec{E}=\left[9 \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{k} V / m\right]\)
2 \(\vec{E}=\left[60 \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{k} V / m\right]\)
3 \(\vec E = \left[ {3 \times {{10}^{ - 8}}\sin \left( {1.6 \times {{10}^3}x + 48 \times {{10}^{10}}t} \right)\hat i\;V/m} \right]\)
4 \(\vec E = \left[ {3 \times {{10}^{ - 8}}\sin \left( {1.6 \times {{10}^3}x + 48 \times {{10}^{10}}t} \right)\hat j\;V/m} \right]\)
PHXI15:WAVES

358958 Magnetic field in plane electromagnetic wave is given by \(\vec{B}=B_{0} \sin (k x+\omega t) \hat{j} T\). Expression for corresponding electric field will be

1 \(\vec{E}=-B_{0} c \sin (k x+\omega t) \hat{k} V / m\)
2 \(\vec{E}=B_{0} c \sin (k x-\omega t) \hat{k} V / m\)
3 \(\vec{E}=B_{0} c \sin (k x+\omega t) \hat{k} V / m\)
4 \(\vec{E}=\dfrac{B_{0}}{c} \sin (k x+\omega t) \hat{k} V / m\)
PHXI15:WAVES

358955 The electric field of an electromagnetic wave in free space is given by:
\({E=10 \cos \left(10^{7} t+k x\right) V / m}\)
where \({t}\) and \({x}\) are in seconds and metres, respectively. It can be inferred that
(a) the wavelength \({\lambda}\) is \(188.4\,m\)
(b) the wave number \({k}\) is \(0.33\,rad/m\)
(c) the wave amplitude is \(10\,V/m\)
(d) the wave is propagating along \({+x}\)-direction.
Which one of the following pairs of statements is correct?

1 (a) and (b)
2 (b) and (c)
3 (a) and (c)
4 (c) and (d)
PHXI15:WAVES

358956 Assertion :
Accelerated charge radiate electromagnetic waves.
Reason :
Oscillating electric and magnetic fields regenerate each other.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI15:WAVES

358957 If the magnetic field in a plane electromagnetic wave is given by
\(\vec{B}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{j} T\), then what will be expression for electric field?

1 \(\vec{E}=\left[9 \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{k} V / m\right]\)
2 \(\vec{E}=\left[60 \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} t\right) \hat{k} V / m\right]\)
3 \(\vec E = \left[ {3 \times {{10}^{ - 8}}\sin \left( {1.6 \times {{10}^3}x + 48 \times {{10}^{10}}t} \right)\hat i\;V/m} \right]\)
4 \(\vec E = \left[ {3 \times {{10}^{ - 8}}\sin \left( {1.6 \times {{10}^3}x + 48 \times {{10}^{10}}t} \right)\hat j\;V/m} \right]\)
PHXI15:WAVES

358958 Magnetic field in plane electromagnetic wave is given by \(\vec{B}=B_{0} \sin (k x+\omega t) \hat{j} T\). Expression for corresponding electric field will be

1 \(\vec{E}=-B_{0} c \sin (k x+\omega t) \hat{k} V / m\)
2 \(\vec{E}=B_{0} c \sin (k x-\omega t) \hat{k} V / m\)
3 \(\vec{E}=B_{0} c \sin (k x+\omega t) \hat{k} V / m\)
4 \(\vec{E}=\dfrac{B_{0}}{c} \sin (k x+\omega t) \hat{k} V / m\)