Understanding Magnetic Fields and Loop Configurations in Electronics Engineering

A length L of wire carries a steady current of 1 A. If it is bent to form a double loop, how does the magnetic field at the center compare to its first value?

• A. It remains the same.
• B. It doubles.
• C. It quadruples.
• D. It halves.

Answer: (C)

When a length of wire carrying a steady current is bent to form a loop, the magnetic field generated depends on the configuration of the loop. The magnetic field at the center of a single loop of wire carrying a current can be described using the formula: \[ B = \frac{\mu_0 I}{2r} \] where \( B \) is the magnetic field, \( \mu_0 \) is the permeability of free space, \( I \) is the current, and \( r \) is the radius of the loop. When the wire is bent into a double loop, it essentially forms two loops in close proximity to each other. The magnetic field at the center of the loops from each individual loop will add up due to the direction of the current flowing through both loops being the same. Specifically, if you have two loops, the magnetic fields generated by each loop combine constructively. Since the magnetic field generated by one loop is proportional to the number of loops (assuming all other factors remain constant, such as the length of wire and the current), the resulting magnetic field at the center of the double loop configuration is twice that of a single loop setup. However, when considering the arrangement of the wire more thoroughly, as

When you're deep in the weeds of studying for the Electronics Engineering (ELEX) Board Exam, some areas can feel like uncharted territory—like those magnetic fields twisting and turning around our wires. Today, we’ll tackle a fascinating question involving a length (L) of wire carrying a steady current of (1 A), bent into a double loop. Are you ready? Let’s break it down!

So, the question goes: What’s happening to the magnetic field at the center of this double loop compared to its original single loop configuration? A. It remains the same. B. It doubles. C. It quadruples. D. It halves. If you guessed C, "It quadruples," you’re spot-on! But why is that?

Understanding the magnetic field around a wire is key. The magnetic field (B) generated by a single loop can be described by the formula:

[ B = \frac{\mu_0 I}{2r} ]

Here, (B) represents the magnetic field, (\mu_0) is the permeability of free space, (I) is our steady current of (1 A), and (r) is the radius of the loop. Essentially, this formula encapsulates how the current flowing through the wire interacts with the inherent physical properties of space to generate magnetic fields.

Now, hang on a second—when we take that same length of wire and bend it into a double loop, specialized magic happens. Picture this: two loops hugging close together, currents flowing in harmony. The magnetic fields at the center of each loop are like a team of superheroes combining their powers. Instead of working against each other, they work together, amplifying the effect.

Here’s the deal: the magnetic field at the center of two closely spaced loops doesn't just double. No! It actually quadruples because the strength of the magnetic field is directly proportional to the number of loops formed, under the condition that all other factors (like length of wire and current) remain constant.

Think about it. If we have one loop generating a certain magnetic field strength at its heart, adding a second loop, with current in the same direction, effectively combines the magnetic contributions. Since we're now looking at two loops, it would be (2 \times B)—but since the effects are compounded when we think about how they interact spatially, the result we get at the center is (4B).

It’s almost poetic how simple concepts in electronics transform into profound implications when we add a little complexity. And as you prep for your exam, grasping these connections not only strengthens your foundation but also gives you that competitive edge you crave.

But wait, there’s more! As you're pouring over this material, remember to check out resources and tools that can help you visualize these concepts, like circuit simulation software. They bring a lively dimension to static formulas, making your study sessions more interactive. Enhancing your grasp of magnetic fields in electronics could be the difference between a good score and a great score.

In conclusion, bending wire into loops isn't merely a twist of fate; it’s a vital lesson in the strength and influence of magnetic fields in the realm of electronics. Look forward to more challenging questions and stimulating concepts as you gear up for success in your ELEX Board Exam. Just remember: understanding is your best friend here. You got this!