In a plane electromagnetic wave, the electric field of amplitude 1 V m-1 varies with time in free space. The average energy density of magnetic field is (in Jm-3)

Question

In a plane electromagnetic wave, the electric field of amplitude 1 V m-1 varies with time in free space. The average energy density of magnetic field is (in Jm-3) (A) 8.86 × 10-12 (B) 4.43 × 10-12 (C) 17.72 × 10-12 (D) 2.21 × 10-12

Tardigrade Admin · Accepted Answer

We know that,
The energy density (energy per unit volume) in an electric field

E

in vacuum

= \frac{1}{2} ε_{0} E^{2}

U = \frac{1}{2} ε_{0} E^{2}

where

ε_{0} = 8.86 \times 1 0^{- 12} C^{2} / N - m^{2}

E = 1 V / m

= \frac{1}{2} \times 8.86 \times 1 0^{- 12} \times (1)^{2}

= 4.43 \times 1 0^{- 12}

So, the average energy density of magnetic field

= \frac{4.43 \times 1 0 ^{- 12}}{2}

= 2.21 \times 1 0^{- 12} J / m^{2}

Q. In a plane electromagnetic wave, the electric field of amplitude $1 V m^{- 1}$ varies with time in free space. The average energy density of magnetic field is (in $J m^{- 3}$ )

$8.86 \times 1 0^{- 12}$

$4.43 \times 1 0^{- 12}$

$17.72 \times 1 0^{- 12}$

$2.21 \times 1 0^{- 12}$

$1.11 \times 1 0^{- 12}$

Q. In a plane electromagnetic wave, the electric field of amplitude 1Vm−1 varies with time in free space. The average energy density of magnetic field is (in Jm−3)

8.86×10−12

4.43×10−12

17.72×10−12

2.21×10−12

1.11×10−12