# Why can't a current carrying loop (curl of the electric field exists) produce a time varying magnetic field?

If a time varying magnetic field can give value to the curl of an electric field, why not the other way round? That is, why can't an enclosed loop with some emf produced (basically a current carrying loop) produce a changing magnetic field?

It does produce a constant magnetic field, yes. But according to Faraday's law, curl E=-dB/dt if the curl of the electric field has a value, shouldn't the time derivative also have a value? Meaning: a changing magnetic field should be produced.

• Could you describe the physical situation you’re considering in more detail please? A closed loop of current has E slumming up to zero around it: there’s not average curl of E. Oct 10, 2019 at 13:18
• It's just a closed loop, like you're mentioning. Oh yes, you're right. I thought that there will be field 'in the wire'. Won't there be a field? Oct 10, 2019 at 13:19
• Are you sure the curl of the electric field is nonzero in this situation? Oct 10, 2019 at 13:23
• I'm not sure. Maybe that's where I'm wrong. But how to think of it to be equal to 0? Oct 10, 2019 at 13:29
• Yes..it is directed along the length of the wire. So the curl for the infinitesimally small area would be 0. Oct 10, 2019 at 13:42