**Induced Electric Fields**

Let us place a copper ring of radius r in a uniform external magnetic field, as in . The field-neglecting fringing-fills a cylindrical volume of radius R. Suppose that we increase the strength of this field at a steady rate, perhaps by increasing – in an appropriate way – the current I the windings of the electromagnet that produces the field. The magnetic flux through the ring will then change at a steady rate and-by Faraday’s law-an induced EMT and thus an induced current will appear in the ring. From Lenz ‘ s law we can deduce that the direction of the induced

current is If there is a current in the copper ring. an electric field must be present along the ring; an electric field is needed to do the work of moving the conduction electrons.Moreover. the electric field must have been produced by the changing magnetic flux.This induced electric field E is just as real as an electric field produced by static charges; either field will exert a force qoE on a particle of charge this line of reasoning. we are led to a useful and informative restatement of Faraday’s law of induction A changing magnetic field produces an electric field. The striking feature of this statement is that the electric field is induced even if then s no coppering.

To fix these ideas, consider, which is just like a except the copper ring has been replaced by a hypothetical circular path of radius r. We assume, as previously, that the magnetic field if is increasing in magnitude at a constant rate dB/dr. The electric field induced at various points around the circular path must-from the symmetry-be tangent to the circle, as Fig. 31-13b shows.* Hence, the circular path is an electric field line. There is nothing special about of radius r, so the electric field lines produced by the changing magnetic field must be a set of concentric circles, as in As long as the magnetic field is increasing with time, the electric field represented by the circular field lines in Fig. 31-13c will be present. If the magnetic field remains constant with time, there will be no induced electric field and thus no electric field lines. If the magnetic field is decreasing with time (at a constant rate), thermoelectric field lines will still be concentric circles as in but they will now have the opposite direction. All this is what we have in mind when we say: “A changing magnetic field produces an electric field.”

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