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Question

The electric field of a plane electromagnetic wave varies with the time of amplitude 2Vm-1propagating along the z-axis. The average energy density of the magnetic field is (inJm-3)


A

13.29×10-12

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B

8.85×10-12

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C

17.72×10-12

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D

4.43×10-12

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E

2.22×10-12

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Solution

The correct option is B

8.85×10-12


Step 1: Given data

Electric field is E=2Vm-1

Step 2: Formula used

The following formula is used to compute the UB=12B2μ1,

Where UB=average energy density of the magnetic field, B0=magnetic field, μ0=vacuum permeability

Speed of light c=1μoεo2

Step 3: Compute the average energy density of the magnetic field

We know that ElectricfieldE=MagneticfieldB×Speedoflightc3

Substitute equation 3 in equation 1.

UB=14E2c2μ4

Substitute equation 2 in equation 4,

UB=14E2μ×1με=14εE2=14×8·85×10-12×22=8.85×10-12Jm3

The average energy density of the magnetic field is 8.85×10-12Jm3

Hence, option B is the correct answer.


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