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?

This question is a beautiful conceptual journey that tests your fundamental understanding of Maxwell's equations and the topological differences between electric and magnetic fields. Let's break down the physics behind each pattern to uncover the truth.

Field lines are a powerful visual tool introduced by Michael Faraday to help us 'see' invisible forces. The density of the lines represents the strength of the field, and the arrows indicate the direction of the force. However, electric and magnetic fields obey very different mathematical rules, which dictate the shapes their field lines can take.

Let's carefully examine patterns (a) and (b). Notice how the lines either radiate outwards from a central point or converge inwards. We immediately recognize these as the electrostatic fields of isolated positive and negative point charges.

But could these represent a magnetic field? Absolutely not! One of the fundamental laws of physics, Gauss's Law for Magnetism, states that magnetic monopoles simply do not exist. Mathematically, this is expressed as:

This equation tells us that the net magnetic flux through any closed surface is always zero. Consequently, magnetic field lines must always form closed loops; they can never start or end at a single point. So, options (a) and (b) are immediately disqualified.

Now, let's skip over to pattern (d). Look at these beautiful closed loops. This is the classic representation of a magnetic dipole field, like what you'd see around a small bar magnet or a current-carrying loop. So it works perfectly for magnetism.

But what about an electric field? Well, an electrostatic field (created by stationary charges) is conservative. Its field lines must originate on positive charges and terminate on negative charges. They never, ever form continuous closed loops. The mathematical statement for this is that the curl of an electrostatic field is zero:

Because electrostatic field lines cannot loop back on themselves, pattern (d) cannot represent an electric field.

Finally, let's focus on pattern (c). Here we have concentric circular loops. We know this perfectly describes the magnetic field around a long, straight, current-carrying wire, as dictated by Ampere's Law.

But here is the catch—can an electric field look like this? Yes, it can! According to Faraday's Law of Electromagnetic Induction, a time-varying magnetic field creates an induced electric field.

Unlike electrostatic fields, these induced electric fields are non-conservative. Because they are generated by a changing magnetic flux rather than stationary charges, they curl around the magnetic field lines and form continuous closed loops, exactly like the ones shown in pattern (c).

Putting it all together, the only field pattern that can physically represent both an electric field (specifically, an induced one) and a magnetic field is the one with closed concentric circles. This makes option (c) our correct answer. It's a brilliant conceptual question that reminds us that while electric and magnetic fields are deeply intertwined, their geometric rules are strictly governed by Maxwell's equations.