Nature of EM Waves & Wave Equation

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$60\,\hat{k}$
• (b)$-60\,\hat{k}$
• (c)$30\,\hat{k}$
• (d)$-600\,\hat{k}$

Nature of EM Waves & Wave Equation · Direction of E, B and propagation

• (a)$\frac{\vec{E}\times\vec{k}}{\omega}$
• (b)$\frac{\vec{k}\times\vec{E}}{\omega}$
• (c)$\omega(\vec{E}\times\vec{k})$
• (d)$\omega(\vec{k}\times\vec{E})$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$\vec{E} = -\nu\lambda B_0\sin\left(2\pi\nu t - \frac{2\pi x}{\lambda}\right)\hat{k}$
• (b)$\vec{E} = -\nu\lambda B_0\sin\left(2\pi\nu t - \frac{2\pi x}{\lambda}\right)\hat{i}$
• (c)$\vec{E} = \nu\lambda B_0\sin\left(2\pi\nu t - \frac{2\pi x}{\lambda}\right)\hat{k}$
• (d)$\vec{E} = \nu\lambda B_0\sin\left(2\pi\nu t - \frac{2\pi x}{\lambda}\right)\hat{i}$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$-1.8\times 10^{-7}\sin(kz - \omega t)\,\hat{i}$ T
• (b)$+1.8\times 10^{-7}\sin(kz - \omega t)\,\hat{i}$ T
• (c)$1.4\times 10^{-7}\sin(kz - \omega t)\,\hat{k}$ T
• (d)$1.4\times 10^{-7}\sin(kz - \omega t)\,\hat{i}$ T

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$B_z = 2.3\times 10^{-7}\sin\left[0.6\times 10^{3}x - 1.8\times 10^{11}t\right]$
• (b)$B_z = 2.3\times 10^{-7}\sin\left[0.6\times 10^{3}x + 1.8\times 10^{11}t\right]$
• (c)$B_y = 2.3\times 10^{-7}\sin\left[0.6\times 10^{3}x - 1.8\times 10^{11}t\right]$
• (d)$B_y = 69\sin\left[0.6\times 10^{3}x + 1.8\times 10^{11}t\right]$

Nature of EM Waves & Wave Equation · Force on a charge

• (a)200
• (b)150
• (c)400
• (d)300

Nature of EM Waves & Wave Equation · Direction of E, B and propagation

• (a)$E_x, B_y$
• (b)$E_y, B_x$
• (c)$E_y, B_z$
• (d)$E_z, B_y$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$B_z = 60\cos\left(5x + 1.5\times 10^{9}t\right)\text{ T}$
• (b)$B_y = 60\sin\left(5x + 1.5\times 10^{9}t\right)\text{ T}$
• (c)$B_y = 2\times 10^{-7}\cos\left(5x + 1.5\times 10^{9}t\right)\text{ T}$
• (d)$B_x = 2\times 10^{-7}\cos\left(5x + 1.5\times 10^{9}t\right)\text{ T}$

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$B_z = 1.55\times 10^{-8}\text{ T}$
• (b)$B_z = 6.2\times 10^{-8}\text{ T}$
• (c)$B_z = 3.1\times 10^{-8}\text{ T}$
• (d)$B_z = 9.3\times 10^{-8}\text{ T}$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$\vec{E} = \left(\frac{1}{2}\hat{i} + \frac{\sqrt{3}}{2}\hat{j}\right)30c\sin\left[\omega\left(t + \frac{z}{c}\right)\right]$
• (b)$\vec{E} = \left(\frac{1}{2}\hat{i} - \frac{\sqrt{3}}{2}\hat{j}\right)30c\sin\left[\omega\left(t - \frac{z}{c}\right)\right]$
• (c)$\vec{E} = \left(\frac{\sqrt{3}}{2}\hat{i} - \frac{1}{2}\hat{j}\right)30c\sin\left[\omega\left(t + \frac{z}{c}\right)\right]$
• (d)$\vec{E} = \left(\frac{3}{4}\hat{i} + \frac{1}{4}\hat{j}\right)30c\cos\left[\omega\left(t - \frac{z}{c}\right)\right]$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$\vec{B} = \frac{57}{3\times 10^{8}}\cos\left[7.5\times 10^{6}t - 5\times 10^{-3}(3x + 4y)\right](\hat{k})$
• (b)$\vec{B} = \frac{57}{3\times 10^{8}}\cos\left[7.5\times 10^{6}t - 5\times 10^{-3}(3x + 4y)\right](5\hat{k})$
• (c)$\vec{B} = -\frac{57}{3\times 10^{8}}\cos\left[7.5\times 10^{6}t - 5\times 10^{-3}(3x + 4y)\right](\hat{k})$
• (d)$\vec{B} = -\frac{57}{3\times 10^{8}}\cos\left[7.5\times 10^{6}t - 5\times 10^{-3}(3x + 4y)\right](5\hat{k})$

Nature of EM Waves & Wave Equation · Nature of EM waves

• (a)They are transverse in nature
• (b)The energy density in electric field is equal to energy density in magnetic field
• (c)They travel with a speed equal to $\frac{1}{\sqrt{\mu_0\varepsilon_0}}$
• (d)They originate from charges moving with uniform speed

Nature of EM Waves & Wave Equation · Reading the wave equation

• (a)2.5
• (b)5
• (c)10
• (d)2

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$9.6\hat{j}\text{ T}$
• (b)$3.2\times 10^{-8}\hat{i}\text{ T}$
• (c)$9.6\times 10^{-8}\hat{k}\text{ T}$
• (d)$3.2\times 10^{-8}\hat{k}\text{ T}$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$E_z = 105\sin\left(1.5\times 10^{3}x + 0.5\times 10^{11}t\right)\text{ V m}^{-1}$
• (b)$E_y = 10.5\sin\left(1.5\times 10^{3}x + 0.5\times 10^{11}t\right)\text{ V m}^{-1}$
• (c)$E_y = 1.17\sin\left(1.5\times 10^{3}x + 0.5\times 10^{11}t\right)\text{ V m}^{-1}$
• (d)$E_z = 1.17\sin\left(1.5\times 10^{3}x + 0.5\times 10^{11}t\right)\text{ V m}^{-1}$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$B_z = 2\times 10^{-7}\sin\left[\frac{\pi}{2}\left(x - 3\times 10^{8}t\right)\right]\hat{k}\text{ T}$
• (b)$B_z = 2\times 10^{-7}\sin\left[\frac{\pi}{2}\times 10^{3}\left(x - 3\times 10^{8}t\right)\right]\hat{k}\text{ T}$
• (c)$B_z = 60\sin\left[\frac{\pi}{2}\left(x - 3\times 10^{8}t\right)\right]\hat{k}\text{ T}$
• (d)$B_x = 60\sin\left[\frac{\pi}{2}\left(x - 3\times 10^{8}t\right)\right]\hat{i}\text{ T}$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$\vec{B} = \hat{j}\frac{40}{c}\cos\omega(t - z/c)$
• (b)$\vec{B} = \hat{i}\frac{40}{c}\cos\omega(t - z/c)$
• (c)$\vec{B} = \hat{j}\,40\cos\omega(t - z/c)$
• (d)$\vec{B} = \hat{k}\frac{40}{c}\cos\omega(t - z/c)$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$\vec{B} = E_0 C\cos(\omega t + kz)\hat{j}$
• (b)$\vec{B} = \frac{E_0}{C}\cos(\omega t - kz)\hat{j}$
• (c)$\vec{B} = E_0 C\cos(\omega t - kz)\hat{j}$
• (d)$\vec{B} = \frac{E_0}{C}\cos(\omega t + kz)\hat{j}$

Nature of EM Waves & Wave Equation · Nature of EM waves

• (a)Electromagnetic waves do not require any medium for their propagation.
• (b)Electromagnetic waves can travel through vacuum with speed of light
• (c)Material medium is necessary for propagation of electromagnetic waves.
• (d)Electromagnetic waves are transverse in nature.

Nature of EM Waves & Wave Equation · Nature of EM waves

• (a)Both Statement I and Statement II are true
• (b)Statement I is true and Statement II is false
• (c)Both Statement I and Statement II are false
• (d)Statement I is false but Statement II is true

Nature of EM Waves & Wave Equation · Direction of E, B and propagation

• (a)at $45^\circ$ angle from positive y-axis
• (b)positive $y$-axis
• (c)negative $y$-axis
• (d)positive z-axis

Nature of EM Waves & Wave Equation · Direction of E, B and propagation

• (a)Negative direction of $y$
• (b)Positive direction of $z$
• (c)Positive direction of $x$
• (d)Negative direction $x$

Nature of EM Waves & Wave Equation · Direction of E, B and propagation

• (a)$\frac{1}{\omega}\left(\vec{K}\times\vec{E}\right)$
• (b)$\vec{K}\times\vec{E}$
• (c)$\omega\left(\vec{K}\times\vec{E}\right)$
• (d)$\omega\left(\vec{E}\times\vec{K}\right)$

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$1.6\times 10^{-8}\text{ T}$
• (b)$1.6\times 10^{-7}\text{ T}$
• (c)$1.6\times 10^{-6}\text{ T}$
• (d)$1.6\times 10^{-9}\text{ T}$

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$-2.2\times 10^{-8}\hat{i}\text{ T}$
• (b)$2.2\times 10^{-8}\hat{i}\text{ T}$
• (c)$2.2\times 10^{-8}\hat{k}\text{ T}$
• (d)$-2.2\times 10^{-8}\hat{k}\text{ T}$

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$6.0\times 10^{-7}\text{ V m}^{-1}$
• (b)$5\times 10^{14}\text{ V m}^{-1}$
• (c)$180\text{ V m}^{-1}$
• (d)$2\times 10^{15}\text{ V m}^{-1}$

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$E_0 B_0 = \omega k$
• (b)$E_0 = k B_0$
• (c)$k E_0 = \omega B_0$
• (d)$\omega E_0 = k B_0$

Nature of EM Waves & Wave Equation · Force on a charge

• (a)$q(\vec{v}\times\vec{B})$
• (b)$q(\vec{B}\times\vec{v})$
• (c)$q(\vec{E}\times\vec{v})$
• (d)$q\vec{E} + q(\vec{v}\times\vec{B})$

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$\frac{\sqrt{\mu_0\varepsilon_0}}{c}$
• (b)c
• (c)$\frac{1}{c}$
• (d)$\frac{c}{\sqrt{\mu_0\varepsilon_0}}$

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$9\ \mu\text{T}$
• (b)$27\ \mu\text{T}$
• (c)$3\ \mu\text{T}$
• (d)$270\text{ GT}$

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$15\times 10^{2}\text{ V m}^{-1}$
• (b)$5\times 10^{-6}\text{ V m}^{-1}$
• (c)$16\times 10^{12}\text{ V m}^{-1}$
• (d)$4\times 10^{2}\text{ V m}^{-1}$

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)18 $\times$ 10 $-$7 T
• (b)54 $\times$ 10$-$7 T
• (c)54 $\times$ 10$-$8 T
• (d)18 $\times$ 10$-$8 T

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)1 $\times$ 10$-$6 T
• (b)5 $\times$ 10$-$6 T
• (c)18 $\times$ 109 T
• (d)21 $\times$ 109 T

Nature of EM Waves & Wave Equation · Nature of EM waves

• (a)(D) only
• (b)(B) and (D) only
• (c)(B), (C) and (E) only
• (d)(A), (B) and (E) only

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$6\text{ V m}^{-1}$ along $x$-axis
• (b)$3\text{ V m}^{-1}$ along $z$-axis
• (c)$6\text{ V m}^{-1}$ along $z$-axis
• (d)$2\times 10^{-8}\text{ V m}^{-1}$ along $z$-axis

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)$+0.8\sin(kz - \omega t)\hat{a}_y + 0.8\sin(kz - \omega t)\hat{a}_x$
• (b)$+1.0\times 10^{-6}\sin(kz - \omega t)\hat{a}_y + 1.5\times 10^{-6}\sin(kz - \omega t)\hat{a}_x$
• (c)$-0.8\sin(kz - \omega t)\hat{a}_y - 1.2\sin(kz - \omega t)\hat{a}_x$
• (d)$-1.0\times 10^{-6}\sin(kz - \omega t)\hat{a}_y - 1.5\times 10^{-6}\sin(kz - \omega t)\hat{a}_x$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$9\cos(1.6\times 10^{3}x + 48\times 10^{10}t)\hat{k}$ V/m
• (b)$3\times 10^{-8}\cos(1.6\times 10^{3}x + 48\times 10^{10}t)\hat{i}$ V/m
• (c)$3\times 10^{-8}\sin(1.6\times 10^{3}x + 48\times 10^{10}t)\hat{i}$ V/m
• (d)$9\sin(1.6\times 10^{3}x - 48\times 10^{10}t)\hat{k}$ V/m

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$E_y = 60\sin\left[\frac{\pi}{4}\times 10^{3}(x - 3\times 10^{8}t)\right]\hat{j}\text{ V m}^{-1}\quad B_z = 2\sin\left[\frac{\pi}{4}\times 10^{3}(x - 3\times 10^{8}t)\right]\hat{k}\text{ T}$
• (b)$E_y = 60\sin\left[\frac{\pi}{4}\times 10^{3}(x - 3\times 10^{8}t)\right]\hat{j}\text{ V m}^{-1}\quad B_z = 2\times 10^{-7}\sin\left[\frac{\pi}{4}\times 10^{3}(x - 3\times 10^{8}t)\right]\hat{k}\text{ T}$
• (c)$E_y = 2\times 10^{-7}\sin\left[\frac{\pi}{4}\times 10^{3}(x - 3\times 10^{8}t)\right]\hat{j}\text{ V m}^{-1}\quad B_z = 60\sin\left[\frac{\pi}{4}\times 10^{3}(x - 3\times 10^{8}t)\right]\hat{k}\text{ T}$
• (d)$E_y = 2\times 10^{-7}\sin\left[\frac{\pi}{4}\times 10^{4}(x - 4\times 10^{8}t)\right]\hat{j}\text{ V m}^{-1}\quad B_z = 60\sin\left[\frac{\pi}{4}\times 10^{4}(x - 4\times 10^{8}t)\right]\hat{k}\text{ T}$

Nature of EM Waves & Wave Equation · Force on a charge

• (a)1: 1
• (b)1: 10
• (c)10: 1
• (d)1: 2

Nature of EM Waves & Wave Equation · Direction of E, B and propagation

• (a)$-\hat{j}+\hat{k},\ -\hat{j}+\hat{k}$
• (b)$\hat{j}+\hat{k},\ \hat{j}+\hat{k}$
• (c)$-\hat{j}+\hat{k},\ -\hat{j}-\hat{k}$
• (d)$\hat{j}+\hat{k},\ -\hat{j}-\hat{k}$

Nature of EM Waves & Wave Equation · Direction of E, B and propagation

• (a)$\left(\hat{k}\right)$
• (b)$\hat{j}$
• (c)$\left(-\hat{k}\right)$
• (d)$\left(-\hat{j}\right)$

Nature of EM Waves & Wave Equation · Direction of E, B and propagation

• (a)Ex, Bz or Ez, Bx
• (b)Ex, By or Ey, Bx
• (c)Ey, By or Ez, Bz
• (d)Ey, Bx or Ex, By

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)0.6 $\hat{j}$ V/m
• (b)6.0 $\hat{k}$ V/m
• (c)6.0 $\hat{j}$ V/m
• (d)0.6 $\hat{k}$ V/m

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

• (a)2.6 $\hat{x}$ V/m
• (b)$-$ 24 $\hat{x}$ V/m
• (c)24 $\hat{x}$ V/m
• (d)$-$2.6 $\hat{y}$ V/m

Nature of EM Waves & Wave Equation · Field values: E0 = cB0

Numerical answer type. Work it out, then open the answer.

Nature of EM Waves & Wave Equation · Force on a charge

• (a)1.28 $\times$ 10$-$18 N
• (b)1.28 $\times$ 10$-$21 N
• (c)12.8 $\times$ 10$-$17 N
• (d)12.8 $\times$ 10$-$18 N

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)The wavelength is 5.4 m
• (b)The frequency of electromagnetic wave is 54 $\times$ 104 Hz.
• (c)The transmitted wave will be $3.1 \cos\left[(1.8)z - (5.4 \times 10^{6})t\right] \hat{i}\text{ N/C}$
• (d)The reflected wave will be $3.1 \cos\left[(1.8)z + (5.4 \times 10^{6})t\right] \hat{i}\text{ N/C}$

Nature of EM Waves & Wave Equation · Force on a charge

• (a)$2\sqrt{2} : 1$
• (b)$1 : \sqrt{2}$
• (c)2: 1
• (d)$\sqrt{2} : 1$

Nature of EM Waves & Wave Equation · Direction of E, B and propagation

• (a)$\frac{1}{\sqrt{5}}\left(\hat{i}+2\hat{j}\right)$
• (b)$\frac{1}{\sqrt{5}}\left(2\hat{i}+\hat{j}\right)$
• (c)$\frac{1}{\sqrt{2}}\left(\hat{i}+\hat{j}\right)$
• (d)$\frac{1}{\sqrt{2}}\left(\hat{j}+\hat{k}\right)$

Nature of EM Waves & Wave Equation · Reading the wave equation

• (a)$\pi\times 10^{-3}\text{ m}$
• (b)$\pi\times 10^{3}\text{ m}$
• (c)$2\times 10^{-3}\text{ m}$
• (d)$2\times 10^{3}\text{ m}$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$\vec{E}(x,t) = \left[36\sin\left(1\times 10^{3}x + 1.5\times 10^{11}t\right)\hat{i}\right]\frac{\text{V}}{\text{m}}$
• (b)$\vec{E}(x,t) = \left[36\sin\left(0.5\times 10^{3}x + 1.5\times 10^{11}t\right)\hat{k}\right]\frac{\text{V}}{\text{m}}$
• (c)$\vec{E}(x,t) = \left[36\sin\left(1\times 10^{3}x + 0.5\times 10^{11}t\right)\hat{j}\right]\frac{\text{V}}{\text{m}}$
• (d)$\vec{E}(x,t) = \left[-36\sin\left(0.5\times 10^{3}x + 1.5\times 10^{11}t\right)\hat{j}\right]\frac{\text{V}}{\text{m}}$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$\frac{E_0}{c}\left(\hat{x} + \hat{y}\right)\sin(kz - \omega t)$
• (b)$\frac{E_0}{c}\left(\hat{x} - \hat{y}\right)\sin(kz - \omega t)$
• (c)$\frac{E_0}{c}\left(\hat{x} - \hat{y}\right)\cos(kz - \omega t)$
• (d)$\frac{E_0}{c}\left(-\hat{x} + \hat{y}\right)\sin(kz - \omega t)$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$\vec{B} = \frac{E_0}{\sqrt{\mu_0\varepsilon_0}}\cos(kx)\hat{j}$
• (b)$\vec{B} = \frac{E_0}{\sqrt{\mu_0\varepsilon_0}}\cos(kx)\hat{k}$
• (c)$\vec{B} = E_0\sqrt{\mu_0\varepsilon_0}\cos(kx)\hat{k}$
• (d)$\vec{B} = E_0\sqrt{\mu_0\varepsilon_0}\cos(kx)\hat{j}$

Nature of EM Waves & Wave Equation · Writing B from E and E from B

• (a)$\vec{E} = -10^{-6}\sin\left[200\pi(y + ct)\right]\hat{k}$ V/m
• (b)$\vec{E} = -9\sin\left[200\pi(y + ct)\right]\hat{k}$ V/m
• (c)$\vec{E} = 9\sin\left[200\pi(y + ct)\right]\hat{k}$ V/m
• (d)$\vec{E} = 3\times 10^{-8}\sin\left[200\pi(y + ct)\right]\hat{k}$