Menghitung Induksi Magnetik: Kawat Lurus & Melingkar Di Titik P

Hey guys! Let's dive into a cool physics problem involving magnetic fields. We're gonna figure out the magnetic induction at a point P due to a long straight wire and a circular wire. This problem often pops up in physics, so understanding it is super helpful. We'll break down the steps, and I'll try to make it as clear as possible. Ready to get started?

Memahami Soal: Kawat Lurus, Melingkar, dan Titik P

Alright, first things first, let's get a grip on what the problem is all about. We've got a long, straight wire that's super long – we can pretty much treat it as infinitely long for our calculations. This straight wire is hanging out near a circular wire. The circular wire has a center, and our point of interest, point P, is chilling somewhere in the vicinity. The key here is that the long wire is really close to the circular wire; in fact, it's touching it. We're given that both wires carry electric currents, and the currents are the same, which is a neat little twist. To make things even more fun, we're given the values of the currents (i₁ and i₂) and the radius of the circular wire. Our goal is to figure out the magnitude and the direction of the magnetic field at point P. Understanding the setup is crucial, so make sure you've visualized the scenario – a long straight wire near a circular loop, with a point P somewhere in the mix.

So, here's the breakdown. We have two sources of magnetic fields: a long, straight wire and a circular wire. Each of these wires, when carrying current, generates its own magnetic field. The magnetic field is a vector quantity, which means it has both magnitude and direction. At point P, the magnetic fields from both wires will combine. Our task is to find the net magnetic field at that point. To do this, we need to calculate the magnetic field produced by each wire separately, and then we'll need to combine them. We'll apply the right-hand rule to figure out the direction of each magnetic field. The right-hand rule is your best friend here! It's a straightforward way to determine the direction of the magnetic field around a current-carrying wire. Also, we'll use the formulas for the magnetic field generated by each type of wire. Don't worry, it's not rocket science, and we'll go through it step by step. Remember, the direction of the magnetic field at P is the net effect of both wires, so the final result can't be determined before we do all the calculations.

One of the most important tips is to always draw a diagram. A good diagram will help you visualize the problem. Draw the straight wire, the circular wire, and point P. Indicate the direction of the current in both wires. Label the radius of the circular wire. Use the right-hand rule to determine the direction of the magnetic field produced by each wire at point P. A clear diagram makes the whole problem much easier to solve.

Menghitung Induksi Magnetik dari Kawat Lurus

Okay, let's start with the long, straight wire. The magnetic field (B₁) produced by a long, straight wire is given by the formula:

B₁ = (μ₀ * i₁) / (2 * π * a)

Where:

• μ₀ is the permeability of free space (a constant, approximately 4π x 10⁻⁷ T·m/A)
• i₁ is the current in the straight wire (given as 5 A)
• a is the distance from the wire to point P. Since the straight wire is touching the circular wire, and P is on the circular wire, the distance 'a' is equal to the radius of the circular wire.

So, first things first, find the distance 'a'. Since the problem states the radius is 10 cm, we should convert this to meters (0.1 m) to match the units of μ₀. Now, let's put the values into the formula and find B₁:

B₁ = (4π x 10⁻⁷ T·m/A * 5 A) / (2 * π * 0.1 m)

B₁ = (20π x 10⁻⁷ T·m) / (0.2π m)

B₁ = 100 x 10⁻⁷ T

B₁ = 1 x 10⁻⁵ T

We've got the magnitude of the magnetic field due to the straight wire. Now, we need to figure out the direction. Use the right-hand rule! Imagine you're grabbing the wire with your right hand, with your thumb pointing in the direction of the current. Your fingers curl in the direction of the magnetic field. For point P, the field is directed into the plane of the circle (away from you if you're looking at the diagram). So, B₁ is directed into the plane of the circle.

Remember that the direction is super important, as it will contribute to our final answer. Also, don't forget to convert all the units to the correct base units. Otherwise, the answer will be totally wrong! Units are your friends in physics; they help you to keep everything straight!

Menghitung Induksi Magnetik dari Kawat Melingkar

Now, let's tackle the circular wire. The magnetic field (B₂) at the center of a circular wire is given by the formula:

B₂ = (μ₀ * i₂) / (2 * r)

Where:

• μ₀ is the permeability of free space (4π x 10⁻⁷ T·m/A)
• i₂ is the current in the circular wire (5 A)
• r is the radius of the circular wire (0.1 m)

Let's plug in the values:

B₂ = (4π x 10⁻⁷ T·m/A * 5 A) / (2 * 0.1 m)

B₂ = (20π x 10⁻⁷ T·m) / (0.2 m)

B₂ = 100π x 10⁻⁷ T

B₂ = π x 10⁻⁵ T

B₂ ≈ 3.14 x 10⁻⁵ T

Again, we need the direction. Use the right-hand rule, but this time, curl your fingers in the direction of the current in the circular loop. Your thumb points in the direction of the magnetic field at the center of the loop. In this case, it's also pointing into the plane of the circle. So, B₂ is also directed into the plane of the circle.

We are on a roll, aren't we? We've found the magnitudes and the directions of the magnetic fields produced by both wires at point P. The hardest part of the problem is over. Now we just need to combine the results!

Menentukan Resultan Induksi Magnetik di Titik P

Since both magnetic fields B₁ and B₂ are pointing in the same direction (into the plane of the circle), we can simply add their magnitudes to find the net magnetic field (B) at point P:

B = B₁ + B₂

B = 1 x 10⁻⁵ T + 3.14 x 10⁻⁵ T

B = 4.14 x 10⁻⁵ T

Therefore, the magnitude of the magnetic field at point P is approximately 4.14 x 10⁻⁵ T, and the direction is into the plane of the circle (or in the negative z-direction if you want to use a coordinate system).

Here's a quick recap: We first calculated the magnetic field from the straight wire, then the magnetic field from the circular wire. Both fields pointed in the same direction, which made the final calculation super easy. We just added the magnitudes to get the total magnetic field. And that's the answer, guys! Congrats on solving the problem!

Remember, these types of problems are about understanding the concepts and applying the right formulas. The right-hand rule is your best friend! Always draw a diagram. Practice with similar problems to reinforce your understanding. Physics is all about practice, and with each problem, you'll get more confident. You've got this!

Kesimpulan

In conclusion, the magnetic induction at point P, which is the contact point between the straight and circular wires, is approximately 4.14 x 10⁻⁵ Tesla, and the direction of the magnetic field is into the plane of the circular wire. The key here was to calculate the magnetic field contribution from each wire separately and recognize that their directions were the same, allowing for a simple addition of their magnitudes. Great job working through this problem! Keep practicing, and you'll become a magnetic field master in no time.