presantion prepared by ibrar ahmad bs physics Induced Electric Fields. om

how we can produce EMF? 1: by changing the magnetic field and keeping the area same induce electric field. 2:by moving conductor and keep the B field constant motional emf. 3:both are in motion relative to each other. om

Time-Varying Magnetic Fields and Induced Electric Fields This show that a changing magnetic flux produces an electric field. This is true not just in conductors, but any-where in space where there is a changing magnetic flux. A Changing Magnetic Flux Produces an Electric Field? how ? om

The previous slide uses an equation (Mr. Ed’s) valid only for a uniform electric field. Let’s see what a more general analysis gives us. Consider a conducting loop of radius r around (but not in) a region where the magnetic field is into the page and increasing (e.g., a solenoid). But the changing magnetic flux induces an emf around the loop.             r The charged particles in the conductor are not in a magnetic field, so they experience no magnetic force. This could be a wire loop around the outside of a solenoid. om

            r The induced emf causes a counter- clockwise current (charges move). But the magnetic field did not accelerate the charged particles (they aren’t in it). Therefore, there must be a tangential electric field around the loop. The work done moving a charged particle once around the loop is. r The sign is positive because the particle’s kinetic energy increases. I E E E E B is increasing. om

            r We can look at work from a different point of view. The electric field exerts a force qE on the charged particle. The instantaneous displacement is always parallel to this force. Thus, the work done by the electric field in moving a charged particle once around the loop is. r The sign is positive because the particle’s displacement and the force are always parallel. I E E E E ds om

            r Summarizing… r I E E E E ds om

            Generalizing still further… r I E E E E ds The loop of wire was just a convenient way for us to visualize the effect of the changing magnetic field. The electric field exists whether or not the loop is present. A changing magnetic flux gives rise to an electric field. om

            But wait…there’s more! A potential energy can be defined only for a conservative force.* *The work done by the force is independent of path. A potential energy is a single-valued function. If this electric field E is due to a conservative force, then the potential energy of a charged particle must be unchanged when it goes once around the loop. E.

But the work done is If we tried to define a potential energy, it would not be single- valued: Work depends on the path! U is not single-valued! We can’t define a U for this E!             E I and F r om

Induced Electric Fields: a summary of the key ideas A changing magnetic flux induces an electric field, as given by Faraday’s Law: This is a different manifestation of the electric field than the one you are familiar with; it is not the electrostatic field caused by the presence of stationary charged particles. Unlike the electrostatic electric field, this “new” electric field is nonconservative. “conservative,” or “Coulomb”“nonconservative” om

Stated slightly differently: we have “discovered” two different ways to generate an electric field. Coulomb Electric Field “Faraday” Electric Field Both “kinds” of electric fields exert forces on charged particles. The Coulomb force is conservative, the “Faraday” force is not. Both “kinds” of electric fields are part of Maxwell’s Equations. om

Direction of Induced Electric Fields The direction of E is in the direction a positively charged particle would be accelerated by the changing flux. Use Lenz’s Law to determine the direction the changing magnetic flux would cause a current to flow. That is the direction of E. om

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