Animated Solution for Physics - Magnetic Effects of Current: Two wires each carrying a steady current $I$ are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II.

A Visual Journey Through Current Configurations

Understanding the magnetic fields produced by different current-carrying structures is a fundamental skill in electromagnetism. In this matrix match problem, we are tasked with analyzing four distinct configurations of wires and determining the resulting magnetic fields and forces. Let's break down each scenario using the Right-Hand Grip Rule.

Parallel Wires

In the first configuration, we have two parallel straight wires carrying steady currents in the same direction. Point $P$ is situated exactly midway between them.

If we apply the Right-Hand Grip Rule to the top wire, we point our thumb in the direction of the current (to the right), and our fingers curl into the page at point $P$. For the bottom wire, curling our fingers around it shows that the magnetic field at $P$ points out of the page.

Since the currents are equal and $P$ is equidistant from both wires, the magnitudes of these two magnetic fields are identical. Because they point in opposite directions, they perfectly cancel each other out. Thus, the net magnetic field at $P$ is zero. Furthermore, parallel wires carrying currents in the same direction attract each other, so they do not repel.

Coaxial Loops with Opposite Currents

Next, we examine two coaxial circular loops carrying currents in opposite directions. Point $P$ lies on their common axis, exactly midway between their centers.

Let's look at the left loop. The current flows clockwise (when viewed from the left). Curling our fingers along this current, our thumb points to the right, indicating the magnetic field at $P$ is directed to the right.

Now, consider the right loop. Its current flows anti-clockwise. However, because it is located on the opposite side of $P$, curling our fingers along its current also results in our thumb pointing to the right! Therefore, the magnetic fields from both loops at point $P$ are in the same direction and add up.

Coaxial Loops with Same Currents

In the third scenario, the two coaxial loops carry currents in the same direction (both clockwise when viewed from the left).

Applying the Right-Hand Grip Rule again, the left loop produces a magnetic field at $P$ directed to the right. The right loop, however, now produces a magnetic field at $P$ directed to the left.

Because the loops are identical and $P$ is exactly in the middle, these two opposing magnetic fields have equal magnitudes and cancel each other out completely. The net magnetic field at $P$ is zero.

Concentric Loops

Finally, we have two coplanar concentric circular loops carrying currents in opposite directions. Point $P$ is their common center.

For the inner loop, the current is clockwise, producing a magnetic field at $P$ that points into the page ($\otimes$). For the outer loop, the current is anti-clockwise, producing a magnetic field at $P$ that points out of the page ($\odot$). Thus, the magnetic fields are in opposite directions.

Additionally, because these concentric loops carry currents in opposite directions, they exert a repulsive magnetic force on each other.

By systematically applying the Right-Hand Grip Rule, we can confidently match the columns: - (A) matches with (q) and (r). - (B) matches with (p). - (C) matches with (q) and (r). - (D) matches with (q) and (s).