Force between Two Parallel Currents: Overview, Questions, Preparation

Let us make this simple. A charged particle moving through a magnetic field doesn’t behave the way you might expect. It doesn’t just keep going in a straight line. Instead, it gets nudged off-course. This nudge isn’t random—it happens in a very particular direction, at a right angle to both the direction the particle is moving and the direction of the field. That is what we call the magnetic force. This effect is formally described by what scientists call the Lorentz force. The basic formula looks like this:

F = q (v × B)

That may look intimidating, but all it is saying is this: if you have got a charge (q) moving with velocity (v) through a magnetic field (B), then it will feel a force (F) pushing it at a right angle. That force can cause the particle to move in a circle, a spiral, or a curve, depending on how it enters the field.

Do remember that, this chapter is also important for CBSE Board exam and NEET exam. 

Now imagine how a charged particle actually moves through a magnetic field. If the charge enters the field straight on, moving perpendicular to it, the force will cause it to loop in a circle. If it moves along the direction of the field, nothing really happens—it just continues on its path. But if it enters at an angle, something interesting occurs. The result is a spiral, or what we call helical motion. This behavior is not just a classroom example. It is how charged particles are trapped in Earth's magnetic field, creating the auroras. It is how cyclotrons and other particle accelerators guide particles during experiments.

Also check: Magnetic field due to a current element

Let us step away from individual particles and talk about current in wires. When electric current flows through a conductor, it creates a magnetic field around it. If you take a loop and move it around the wire, you’ll find that the total magnetic field along the loop is related to the current passing through. This idea is captured in Ampere's Circuital Law.

In simpler terms, this law helps you calculate magnetic fields when the current has some sort of symmetry. For example, it helps you find the field around a long straight wire or inside a solenoid. The law itself is written like this:

∮ B · dl = μ₀ I_enclosed

That expression might look complex, but here is what it means. If you walk in a loop around a wire and measure the magnetic field as you go, the total you measure is directly proportional to how much current is flowing through the wire inside that loop. This law makes it possible to predict magnetic fields without calculating every little piece of the wire.

Speaking of magnetic fields, there is one device that makes great use of them: the solenoid. A solenoid is just a long coil of wire. When electric current flows through it, it produces a magnetic field that is strong and very uniform inside the coil. The more loops and the more current, the stronger the field.

Solenoids are incredibly useful. They are used in relays, electromagnets, and even medical imaging devices. The field inside a long solenoid is given by a simple expression:

B = μ₀ n I

Where n is the number of turns per unit length and I is the current. What is amazing about solenoids is how clean and predictable the magnetic field inside them is, which makes them perfect for experiments and applications that need a stable field.

Now let us consider what happens when we place a loop of current in a magnetic field. That loop experiences torque. It wants to rotate to align with the magnetic field, just like a compass needle aligns with Earth's magnetic field. This torque is what drives electric motors and powers instruments like galvanometers.

The strength of the rotation depends on the magnetic dipole moment of the loop, which is defined as:

μ = I × A

Here, I is the current and A is the area of the loop. The torque the loop feels is then given by:

τ = μ × B

This principle is behind much of the rotation-based motion in modern machines.

Finally, consider a circular loop of wire with current flowing through it. What does the magnetic field look like along the central axis of the loop? It is strongest at the center and decreases as you move further away. You can calculate the field using:

B = (μ₀ I R²) / (2(R² + x²)^(3/2))

Here, R is the radius of the loop and x is the distance from the center along the axis. This setup is not just theoretical—it is how magnetic coils are designed in everything from speakers to lab-grade field generators.

At first glance, magnetic fields might seem mysterious. They don’t push or pull like a rope or a spring. But they influence motion in precise, consistent ways. Whether it is a single electron curving through a lab is magnetic trap or a loop of wire spinning inside a motor, the physics is grounded in these concepts.

Understanding moving charges and magnetism means understanding how we convert electricity into motion, build stable magnetic environments, and harness the forces that power nearly every electronic device around us. Since this chapter holds a decent weightage in JEE exam, it is important to practice NCERT solutions of Moving Charges and Magnetism chapter for a stronger foundation.