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Why is that the emf induced at a point outside a loop equal to the rate of change of magnetic flux inside the loop.

Why is that the emf induced at a point outside a loop equal to the rate of change of magnetic flux inside the loop.

Grade:12th pass

1 Answers

dolly bhatia
200 Points
2 years ago

If you move a wire through a magnetic field so that the wire, the motion and the magnetic field are all mutually orthogonal, them there is a magnetic force on the charges (because of the motion) that has a component in the direction of the wire (because we arranged the directions the right way). The energy comes from the agent moving the wire but there is a real force.

When electric and magnetic forces were considered separate, it was merely an experimentally observed fact that if you changed the magnetic field in time there would be a force driving the charges through a wire. But if you look at that magnetic force above, but consider the situation in the frame of the moving wire, there is no magnetic force in that frame, but there is still a force.

One can consider that to be the real reason that changing magnetic fields induce electric fields. 

To produce EMF, we need to drive electrons or we need to produce a net charge difference at the ends of conductor.  A moving charged particle will experience force by a magnetic field, so, if we are talking about dc machines, the magnetic field produced by the fieldcoil remains constant, that is, no force is experienced by electrons of the wire. So, we have to produce a relative motion between magnetic field and electrons. Whenever the flux passing through the coil changes by any way (like either changing angle, magnetic field or area of coil), we are actually producing a relative motion between electrons and magnetic field. As a result, the electrons experience a magnetic force and shift to produce EMF.

Change is the law of nature but no one likes sudden changes. One may call it analogous to the first law of Newton relating to inertias. In the similar way, suppose a loop is kept in a magnetic field with a magnitude of B tesla. B may be equal to zero. We also use crosses and dots in a plane to show magnetic flux density. Suppose a total of 5 crosses representing B tesla, is passing through the loop. Now, if we

  1. Increase magnetic field say, as a function of time: The loop had learned to live with 5 crosses (x), but now it has say 6 (x). It must have to find a way to get back in the position of 5 (x)and to do that it induces current in such a direction which produces dots (•) inside the loop, watching from outside the computer screen, the current should be anticlockwise (according to screw rule).

  2. Magnetic field decreases:In the second scenario, suppose crosses decrease to 3. Then loop will induce a clockwise current to bring in some crosses to get back to the position of 5 x.

  3. Area of the loop changes:Yes, this can also change the flux and inturn induce current. Flux is defined as 

    Magnetic flux = (magnetic field)(area) cos theta, where theta is angle between area and field vector. EMF induced is the derivative of magnetic flux. So, if area changes - flux changes and thus emf has a non-zero value. Again, this could be easily understood by the above theory as again the number of dots and crosses changes giving rise to current. Neither magnetic field changes nor area.  Magnetic flux remains constant.

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