Animated Solution for Physics - Electromagnetic Induction: Which of the field patterns given in the figure is valid for electric field as well as for magnetic field?

When Electric and Magnetic Lines Look Alike

Have you ever looked at a diagram of field lines and wondered, "Is this an electric field or a magnetic field?" Most of the time, the answer is obvious. But sometimes, nature plays a beautiful trick on us, and the two fields can look exactly identical. Let's dive into this fascinating problem and uncover the physics behind it.

Let's start by examining the fundamental nature of magnetic fields. According to Gauss's Law for Magnetism, magnetic monopoles do not exist. In mathematical terms, this is expressed as:

This elegant equation tells us a profound truth: magnetic field lines can never originate from a single point, nor can they terminate at a single point. They have no beginning and no end. Therefore, magnetic field lines must always form continuous, closed loops.

When we look at the options provided in the question, patterns (a) and (b) show lines radiating outwards or inwards from a central point. Because they don't form closed loops, we can immediately rule them out as candidates for a magnetic field.

So, what do patterns (a) and (b) represent? They are the classic representations of static electric fields. An isolated positive point charge creates field lines that radiate outwards to infinity (pattern a), while a negative point charge creates field lines that point inwards (pattern b).

Static electric fields are created by stationary charges. These fields are conservative, meaning the work done in moving a charge around any closed path is zero:

Because of this conservative nature, static electric field lines can never form closed loops. If they did, a charge moving along that loop would continuously gain energy, violating the law of conservation of energy!

This brings us to a critical crossroads. If static electric fields can't form closed loops, how can any pattern represent both an electric and a magnetic field?

The secret lies in Faraday's Law of Induction. When a magnetic field changes over time, it does something magical: it creates an electric field out of thin air. This is expressed by the Maxwell-Faraday equation:

Unlike the static electric fields created by charges, this induced electric field is non-conservative. Because its curl is non-zero, its field lines actually do form closed loops, exactly like a magnetic field!

Now, let's look at pattern (c). It displays perfect, concentric circular loops.

First, can this be a magnetic field? Absolutely. This is the exact shape of the magnetic field generated by a steady current flowing through a long, straight wire.

Second, can this be an electric field? Yes! If you have a cylindrical region of space where a uniform magnetic field is increasing or decreasing over time, the induced electric field lines will form these exact concentric circles.

Therefore, the concentric circular pattern is the beautiful intersection where the geometry of magnetism and the magic of electromagnetic induction meet. It is the only pattern valid for both fields.