# How can changing magnetic field produce instantaneously the electric field and vice versa? [duplicate]

Maxwell's curl equation for electric field says that time varying magnetic field produces electric field instantaneously but nothing can happen instantaneously according to special relativity. What is the mistake in my understanding since Maxwell's equations are accepted?

Since nothing can happen instantaneously so how is changing magnetic field producing the electric field instantaneously in EM wave according to $$E(x,t) = E_\text{max} \cos(kx - \omega t+\phi)$$
$$B(x,t) = B_\text{max}cos(kx - ωt + \phi)$$ which shows that they are in phase(means no delay)? I feel there should be some delay in wave of electric field as nothing is instantaneous( vice versa if changing electric field).

Edit: the argument I am giving here is different from the question mentioned in possible duplicate. I am asking about instantaneous production of field and not about how they have same expressions.

## marked as duplicate by garyp, John Rennie electromagnetism StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jul 9 at 11:52

• "Maxwell's curl equation for electric field says that time varying magnetic field produces electric field instantaneously" This is the mistake. There is no production per se: electric and magnetic fields are two manifestations of the electromagnetic tensor. What the equations say is more that a variation of one field is $accompanied$ by (a curl) of the other field; but this only describes the relation between the different element of a unique entity, the electromagnetic tensor, without a cause and effect relation. See en.wikipedia.org/wiki/Jefimenko%27s_equations#Discussion – David Jul 9 at 11:15