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A plane electromagnetic wave of frequency 500 MHz is travelling in a vacuum along a y-direction.

At a particular point in space and time, `vec"B"` = 8.0 × 10^{-8} `hat"Z"`T. The value of the electric field at this point is ______.

(speed of light = 3 × 10^{8} ms^{-1})

`hat x, hat y, hat z` are unit vectors along x, y, and Z directions.

#### Options

2.6`hatx"V"/"m"`

`-2.6haty"V"/"m"`

24`hatx"V"/"m"`

-24`hatx"V"/"m"`

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#### Solution

The value of the electric field at this point is `bb(-24hatx"V"/"m")`.

**Explanation:**

Given,

`vec"B"` = 8 × 10^{-8} `hatz`T and c = 3 × 10^{8} m/s

Using the relation

E = Bc = (8 × 10^{-8}) (3 × 10^{8}) = 24

**Given:** Electromagnetic wave travels in a direction along the y-axis.

Since, E × B = c;

Magnetic Field B is along the z-axis and the wave travels along the y-axis.

So, `(-hatx) xx(hatz) = haty"`

The electric field, E will be along the negative x direction.

Hence, `vec"E"` = -24 `hatx` V/m.

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