# I Is the curl of a vector perpendicular to the vector?

1. Jun 7, 2017

### Pushoam

I am asking this because ∇ is also considered as a vector in some cases. Considering it as a vector in this case ,too,
( ∇× E).E = (- ∂ B/∂t).E = - ∂ (B.E)/∂t =0

Since B and E could be arbitrarily dependent on t,
B.E = 0

where B and E are magnetic and electric fields respectively.
This means that B and E are always perpendicular to each other.

2. Jun 7, 2017

### Staff: Mentor

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