A long straight wire carries 2.5 A along the +x-axis. Find the magnitude and direction of the magnetic
field at the point 15 cm in the + y axis direction.

To find the magnitude and direction of the magnetic field created by a long straight wire carrying a current, we use the Biot-Savart law, which simplifies to Ampère's law for this scenario. The formula for the magnetic field \( B \) at a distance \( r \) from a long straight wire carrying current \( I \) is given by:

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

where:
- \( \mu_0 \) is the permeability of free space (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T} \cdot \text{m} / \text{A} \))
- \( I \) is the current through the wire
- \( r \) is the distance from the wire to the point where the magnetic field is being calculated

Given:
- \( I = 2.5 \, \text{A} \)
- \( r = 15 \, \text{cm} = 0.15 \, \text{m} \)

We substitute these values into the formula:

\[ B = \frac{4 \pi \times 10^{-7} \times 2.5}{2 \pi \times 0.15} \]

Simplify the expression:

\[ B = \frac{10^{-6} \times 2.5}{0.15} \]

\[ B = \frac{2.5 \times 10^{-6}}{0.15} \]

\[ B = \frac{2.5}{0.15} \times 10^{-6} \]

\[ B \approx 16.67 \times 10^{-6} \, \text{T} \]

\[ B \approx 16.67 \, \mu\text{T} \]

So, the magnitude of the magnetic field at the point 15 cm in the +y-axis direction is approximately \( 16.67 \, \mu\text{T} \).

The direction of the magnetic field due to a current-carrying wire is given by the right-hand rule. Point the thumb of your right hand in the direction of the current (+x-axis), and your fingers will curl in the direction of the magnetic field. Therefore, at a point on the +y-axis, the magnetic field will be directed into the page (or screen), which corresponds to the negative z-axis direction.

In summary:

- **Magnitude**: \( 16.67 \, \mu\text{T} \)
- **Direction**: Into the page (negative z-axis)

Would you like more details or have any questions?

Here are five questions you can ask:
1. How is the Biot-Savart law derived?
2. What is Ampère's law and how is it applied in different scenarios?
3. Can you explain the right-hand rule in more detail?
4. How does the magnetic field vary with distance from the wire?
5. What happens to the magnetic field if the current in the wire is reversed?

**Tip:** When working with magnetic fields, always remember to use the right-hand rule to determine the direction of the field lines around a current-carrying conductor.

Learn how to calculate the magnetic field created by a long straight wire carrying 2.5 A at a point 15 cm in the +y direction. Utilizes the Biot-Savart law and Ampère's law with detailed step-by-step solution and application of right-hand rule. Suitable for advanced high school or college-level physics.

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