# magnetic flux and EMF - in an open circuit

Lets say I've got a rectangular conducting frame resting inside a changing uniform magnetic field.

the magnetic flux (Φ) is: the vector of the magnetic field cross product the vector of the area of the frame =>

B x A

Now let's say that the angle between the vectors is 90 so they perpendicular. so now is only |B|*|A| (the product of the lengths)

vector B pointing into the page and the frame is laying flat on the page.

here is a representation:

Now we see the that there is a change in the magnetic flux caused by the change in the magnetic field, and this is inducing EMF (ε) in the frame. =>

ε = n * dΦ/dt

we can now define the direction of the current with Lenz's law => lets say the magnetic field is getting stronger then the direction of the current would be counter-clockwise.

but what happens if we remove one side of the frame?

Now there must be no current flowing but is there any EMF induced? any force taking place? what happens?

• First, we choose some path in space for which we want to calculate EMF. For example, path from one terminal to another, which is not close. Then, calculate line integral of electric field $\int \mathbf E\cdot d\mathbf s$ along this path. For close path, this gives the same value as $\frac{d\Phi}{dt}$. – Ján Lalinský Apr 1 '19 at 0:07