EMF vs Potential difference

Electricity and Magnetism Level 2

A circular loop of radius $R$ is placed in a region of uniform time varying magnetic field $B=B_0t$ . The magnetic field is into the plane of the ring. There are two points $A$ and $B$ diametrically opposite to each other on the ring, as shown in the diagram.

What is the potential difference between points $A$ and $B$ ?

Details and Assumptions:

The circular loop has uniform thickness and resistivity.
$B_0$ is a constant and $t$ is time.

0

B_0 \pi R^2

\dfrac{B_0 \pi R^2}{2}

1 solution

Rohit Gupta
Jan 17, 2017

Let the emf induced in the loop be $\varepsilon$ , then the current in the loop will be $i=\dfrac{\varepsilon}{r}$ . Here $r$ is the resistance of the loop.

The potential difference between points $A$ and $B$ will be
$\Delta v = \varepsilon_{AB} - ir_{AB}.$
As the arc $AB$ is half the ring, $\varepsilon_{AB} = \dfrac{ \varepsilon }{2}$ and $r_{AB}=\dfrac{r}{2}$ .
Plugging in the values,
$\Delta v = \dfrac{\varepsilon}{2} - \dfrac{\varepsilon}{r}\dfrac{r}{2} = \boxed 0 .$

Then why does a current flow between A and B? if their P.D is 0?

Anirudh Sreekumar - 4 years, 4 months ago

Now that is a good question,
Let me try to answer it.
There are two electric fields, 1) conservative and 2) Non conservative
1) Conservative field will be the electrostatic field which is produced due to accumulation of static charges. This causes a potential difference which can be created only due to the conservative field. In this case, no charges will be accumulated and the electrostatic field and hence the potential difference will be zero.
2) Non conservative field: This field is due to variable magnetic flux. It is called the induced electric field. It do not create a potential rather it creates an emf. Therefore, there is an emf but no potential difference.

For the current to flow, electric field is required and it does not matter whether the field is electrostatic field or the induced electric field.
Hence, the current is flowing in this circuit and still the potential difference is zero.
And yes, the ohm law is not followed here as it follows only for conservative field.

Rohit Gupta - 4 years, 4 months ago

EMF vs Potential difference

1 solution

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