Magnetic field in a plane electromagnetic wave is given by
`bar(B) = B_(0)"sin"(kx + omegat)hat(j)T`
Expression for corresponding electric field will be

Options

A. `vecE=-B_(0)C sin (Kx+omegat)hatkV//m`
B. `vecE=B_(0)C sin (Kx-omegat)hatkV//m`
C. `vecE=B_(0)C sin (Kx+omegat)hatkV//m`
D. `vecE=(B_(0))/(c)sin(kx+omegat)hatkV//m`

Answer

To find the expression for the electric field corresponding to the given magnetic field in a plane electromagnetic wave, we can follow these steps:

### Step 1: Understand the relationship between electric and magnetic fields in electromagnetic waves.
In an electromagnetic wave, the electric field (E) and the magnetic field (B) are related by the equation:
\[ \frac{E}{B} = c \]
where \( c \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \, \text{m/s} \).

### Step 2: Write down the given magnetic field.
The magnetic field is given as:
\[ \bar{B} = B_0 \sin(kx + \omega t) \hat{j} \]
where \( B_0 \) is the amplitude of the magnetic field, \( k \) is the wave number, and \( \omega \) is the angular frequency.

### Step 3: Calculate the electric field magnitude.
Using the relationship from Step 1, we can express the electric field as:
\[ E = cB \]
Substituting the expression for \( B \):
\[ E = cB_0 \sin(kx + \omega t) \]

### Step 4: Determine the direction of the electric field.
In electromagnetic waves, the electric field is perpendicular to the magnetic field. Given that the magnetic field is in the \( \hat{j} \) direction, the electric field will be in the \( \hat{i} \) direction (assuming the wave is propagating in the \( \hat{i} \) direction).

### Step 5: Write the final expression for the electric field.
Thus, the electric field can be expressed as:
\[ \bar{E} = cB_0 \sin(kx + \omega t) \hat{i} \]

### Final Answer:
The expression for the electric field corresponding to the given magnetic field is:
\[ \bar{E} = cB_0 \sin(kx + \omega t) \hat{i} \]

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