What does direction of EMF mean?

Question

In faraday's law it mention's direction of EMF( like in closed loopit is clockwise or anticlockwise depending on direction of motion of magnet) but defination of EMF is roughly Potential diffrence between two points then what does flow of EMF make any sense in faraday's law?

Answer 1

When you change the magnetic flux through a surface bounded by a closed loop an emf is induced in the loop. That means that if a test charge is taken once around the loop in one direction, the work done per unit charge on the test charge by the electric field that curls round the changing magnetic field is, by definition, the emf. The direction of the emf is that of the electric field. If the loop is an actual loop made of an electrically conducting material, then charge will flow round by itself, in the direction of the emf. In this case the work that has to be done against resistive forces is supplied by the emf.

No potential differences are involved. In fact the whole notion of potential difference is inapplicable to this situation. Potential differences arise from static or quasi-static charges, and you don't have these here.

However if you had a conducting loop with a gap in it, and certain configurations of changing magnetic flux, the emf can make electrons pile up on one cut end of the loop, leaving the other end depleted of electrons and positive. We would then have quasi static charges and a potential difference between the ends. [Electrons will stop flowing, even if there is still changing magnetic flux, when the electric field in the ring due to this changing flux is balanced by the opposing electric field due to the charge separation.] Note that even in this case, where there is a pd, the direction of the emf may be defined independently of the notion of pd.

Answer 2

but defination of EMF is roughly Potential diffrence between two points

There is a "potential difference" only if there is a "potential". How does an electric potential arise? According to Maxwell's/Heaviside's equations (the equations we know today were first formulated by Heaviside based upon Maxwell's work)

$$\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$$

if, and only if $\frac{\partial \vec{B}}{\partial t} = 0$ does $\nabla \times \vec{E}= 0$

If $\nabla \times \vec{E} = 0$ then $E$ is a conservative field, and consequently there exists a scalar potential field $V$ such that

$$E = -\nabla V$$

Thus, when there is no time-varying magnetic field, then there is a well defined scalar potential, and hence "potential differences". [Actually, there are many possible scalar potential fields, each differing from each other by a constant. But when we take a potential difference, those constants don't matter]. When there is a time-varying magnetic field, then there is a path dependent "voltage drop", however, there is not a path independent "potential difference".

So, in the case of electromagnetic induction, we must cast aside the notion that EMF is equal to "potential difference". A suitable definition of EMF in the case of electromagnetic induction is

$$ \mathscr E_{induced} = {\int_a^b}_C \vec{E_{rot}} \cdot d\vec{\ell}$$

where

• $\vec{E_{rot}}$ is the divergence free (or rotational) component of the $\vec{E}$ field, and is a solution to the equation

$$\vec{\nabla} \times \vec{E_{rot}} = \frac{\partial\vec{B}}{\partial t}$$

• the integral is taken from a point $a$ on the wire to a point $b$ on the wire along the wire path $C$

then what does flow of EMF make any sense in faraday's law?

There are two cases. If we form a closed loop, the equation above becomes

$$ \mathscr E_{induced} = {\oint}_C \vec{E_{rot}} \cdot d\vec{\ell}$$

However, because a closed loop integral of a conservative vector field is 0, we can integrate over $\vec{E}$ rather than $\vec{E_{rot}}$ and get the same answer. [$\vec{E}$ is just the sum of $\vec{E_{rot}}$ and a conservative vector field.]

$$ \mathscr E_{induced} = {\oint}_C \vec{E} \cdot d\vec{\ell}$$

Or one can use the non-loop equation

$$ \mathscr E_{induced} = {\int_a^b}_C \vec{E_{rot}} \cdot d\vec{\ell}$$

with Kirchhoff's voltage law to solve a loop where there may be different currents in different sections, but between nodes $a$ and $b$ along curve $C$, there is uniform current.

Answer 3

The "direction" or polarity of a source emf is taken to be the direction it causes an electric current to flow. Since electric current is defined in terms of the motion of positively charged particles, it is the direction that positive charges are pushed.