A doubt in Vector Analysis using dot product...

[Bhanumurthy]

How E.εd/dt(E) = ε/2 E².

 

[subharpe]

is it at all?

I think it is
E.εd/dt(E) = d/dt(ε/2 E²)

 

[Bhanumurthy]

Yeah, iam sorry for the mistake.Subharpe u'r expression is correct.Can u explain that...

 

[subharpe]

d/dt(E.E) = 2E.d/dt(E). This is how it comes....

 

[sreevyas]

d/dt(ε/2 E²)
ε is constant
ε/2 d/dt(E.E)=ε/2[ E.d/dt(E)+d/dt(E).E]
here diffentiation is scalar product
=ε/2[2.E.d/dt( E)]=εd/dt(E)