A Changing Magnetic Flux Generates An Electric Field
A Changing Magnetic Flux Generates An Electric Field
A Changing Magnetic Flux Generates An Electric Field
We know that a changing magnetic flux produces an induced electric current in a conducting loop; the changing magnetic flux creates an electric field which drives electric charges around the conducting loop.
Does a changing magnetic flux create an electric field in empty space, even when no charges are present ?? Yes !!
The fundamental electromagnetic induction effect is that
W=
where q0 E is the magnitude of the force acting on the charged particle and 2r is the distance over the path . Since EMF is related to work by We find that
More generally, we can re-write the above work equation to give the work done on a particle moving along any closed path.
Substituting for W for q0 , we have
It simply says that a changing magnetic field induces an electric field In this form, this equation can be applied to any closed path that can be drawn in a changing magnetic field Does the left side of this equation seem odd for some reason ??
Consider what happens to charged particle that makes a single journey around the circular path in the figure to the right. When it returns to the starting point, it has gain potential (a EMF). This means the same point could have different values of potential. We must conclude that potential has no meaning inside induced electric fields.
However, if a path starts at some point outside an induced electric field region, enters the region and then ends at some point outside this region, an unique potential value can be assigned to this particular path.
where N is the number of turns. The windings of the inductor are said to be linked by the shared flux and the product N is called magnetic flux linkage. The inductance is a measure of flux linkage produce by the inductor per unit current i.
Now, lets consider a long solenoid of cross-section A. What is the inductance per unit length near its middle ??
1st we must calculate the flux linkage N set up by the current in the solenoid. Consider a length l near the middle of the solenoid. The flux linkage for this section is
N = (nl)(BA)
where n is the number of turns per unit length and B is the magnetic field within the solenoid Recall the relationship magnetic field and current in a solenoid is given by
B = 0 i n
Therefore,the inductance per unit length for a long solenoid near the center is
The inductance like capacitance only depends on the geometry
Note the n2, the B field and flux linkage both explicitly depend the winding density