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Show that the avearge energy density of ...

Show that the avearge energy density of the electric field `vecE` equals the average energy density of the magnetic field `vecB`, in electromagnetic waves.

Text Solution

Verified by Experts

`U_(E)=1/4varepsilon_(0)E_(0)^(2)`
Average energy density of B
`U_(B) = 1/4B_(0)/mu_(0)`
`because C = E_(0)/B_(0)` So,
`U_(E)=1/4varepsilon_(0)(cB_(0))^(2)=1/4varepsilon_(0)c^(2)B_(0)^(2)=1/4varepsilon_(0)1/((mu_(0)varepsilon_(0)))xxB_(0)^(2)`
`=1/4B_(0)^(2)/mu_(0)`
`U_(E)=U_(B)`
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