A magnetic field vector in an electromagnetic wave is represented by, Its associated electric field vector is

Question

A magnetic field vector in an electromagnetic wave is represented by, $\vec{B} = B_{0} \sin (2 π ν t - \frac{2 π x}{λ}) \hat{j} .$ Its associated electric field vector is ______. [2026]

Smart Achievers · Accepted Answer

(1)

$\hat{E} \times \hat{B} = \hat{c}$

$light is moving along + x direction.$

$\hat{B} = \hat{j} and \hat{c} = \hat{i}$

$∴$ $\hat{E} = - \hat{k}$

$\frac{E_{0}}{B_{0}} = c = ν λ$

$E_{0} = B_{0} \times ν λ$

$\vec{E} = B_{0} λ ν \cdot \sin (2 π ν t - \frac{2 π}{λ} x) (- \hat{k})$

$= - ν λ B_{0} \sin (2 π ν t - \frac{2 π}{λ} x) \hat{k}$

Solution

Q.
A magnetic field vector in an electromagnetic wave is represented by, $\vec{B} = B_{0} \sin (2 π ν t - \frac{2 π x}{λ}) \hat{j} .$ Its associated electric field vector is ______. [2026]

1 $\vec{E} = - ν λ B_{0} \sin (2 π ν t - \frac{2 π x}{λ}) \hat{k}$

2 $\vec{E} = - ν λ B_{0} \sin (2 π ν t - \frac{2 π x}{λ}) \hat{i}$

3 $\vec{E} = ν λ B_{0} \sin (2 π ν t - \frac{2 π x}{λ}) \hat{k}$

4 $\vec{E} = ν λ B_{0} \sin (2 π ν t - \frac{2 π x}{λ}) \hat{i}$

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Solution

Q. A magnetic field vector in an electromagnetic wave is represented by, B→=B0sin(2πνt-2πxλ)j^. Its associated electric field vector is ______. [2026]

1 E→=-νλB0sin(2πνt-2πxλ)k^

2 E→=-νλB0sin(2πνt-2πxλ)i^

3 E→=νλB0sin(2πνt-2πxλ)k^

4 E→=νλB0sin(2πνt-2πxλ)i^