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In an electromagnetic wave, the electric...

In an electromagnetic wave, the electric field oscillates sinusoidally with amplitude `48 Vm^(-1)`, the RMS value of oscillating magnetic field will be nearly equal to :

A

`1.6 xx 10^(-8) T`

B

`16 xx 10^(-9) T`

C

`144 xx 10^(8) T`

D

`11.3 xx 10^(-8) T`

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The correct Answer is:
To find the RMS value of the oscillating magnetic field in an electromagnetic wave where the electric field oscillates sinusoidally with a given amplitude, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the given parameters:** - The amplitude of the electric field \( E_0 = 48 \, \text{V/m} \). 2. **Use the relationship between the electric field and magnetic field in an electromagnetic wave:** - The relationship is given by: \[ B_0 = \frac{E_0}{c} \] where \( B_0 \) is the amplitude of the magnetic field and \( c \) is the speed of light in vacuum, approximately \( c = 3 \times 10^8 \, \text{m/s} \). 3. **Calculate the amplitude of the magnetic field:** - Substitute the values into the equation: \[ B_0 = \frac{48 \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} = \frac{48}{3 \times 10^8} \, \text{T} \] - Performing the division: \[ B_0 = 16 \times 10^{-8} \, \text{T} \] 4. **Calculate the RMS value of the magnetic field:** - The RMS value \( B_{\text{rms}} \) is related to the amplitude \( B_0 \) by: \[ B_{\text{rms}} = \frac{B_0}{\sqrt{2}} \] - Substitute \( B_0 \): \[ B_{\text{rms}} = \frac{16 \times 10^{-8}}{\sqrt{2}} \, \text{T} \] - Calculate \( \sqrt{2} \approx 1.414 \): \[ B_{\text{rms}} \approx \frac{16 \times 10^{-8}}{1.414} \approx 11.31 \times 10^{-8} \, \text{T} \] 5. **Final answer:** - The RMS value of the oscillating magnetic field is approximately: \[ B_{\text{rms}} \approx 11.31 \times 10^{-8} \, \text{T} \]

To find the RMS value of the oscillating magnetic field in an electromagnetic wave where the electric field oscillates sinusoidally with a given amplitude, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the given parameters:** - The amplitude of the electric field \( E_0 = 48 \, \text{V/m} \). 2. **Use the relationship between the electric field and magnetic field in an electromagnetic wave:** ...
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