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Can you explain why I1 is out of the page and I2 is into the page 

To understand why \( I_1 \) is out of the page and \( I_2 \) is into the page, let's go over the context of the magnetic field directions generated by these currents.

1. **Direction of Magnetic Field from a Current-Carrying Wire**: According to the right-hand rule, if you point your right thumb in the direction of the current, your curled fingers show the direction of the magnetic field around the wire. 

2. **Position of Point \( P \)**: In this problem, point \( P \) is located to the right of both wires, with distances given as \( r_1 = 2.0 \, \text{cm} \) from \( I_1 \) and \( r_2 = 1.0 \, \text{cm} \) from \( I_2 \).

3. **Current Directions and Magnetic Field Contribution**:
   - For \( I_1 \): Since the current \( I_1 \) is flowing downward, when you apply the right-hand rule, the magnetic field generated by \( I_1 \) at point \( P \) will point **out of the page**.
   - For \( I_2 \): Since the current \( I_2 \) is flowing upward, using the right-hand rule, the magnetic field generated by \( I_2 \) at point \( P \) will point **into the page**.

4. **Combining the Magnetic Fields**: The total magnetic field at point \( P \) is the vector sum of the magnetic fields from both wires. In the calculations provided:
   - \( B_1 \) (from \( I_1 \)) is \( 4 \times 10^{-5} \, \text{T} \), directed out of the page.
   - \( B_2 \) (from \( I_2 \)) is \( 8 \times 10^{-5} \, \text{T} \), directed into the page.
   - The net magnetic field \( B \) is therefore \( -4 \times 10^{-5} \, \text{T} \) (or \( 4 \times 10^{-5} \, \text{T} \) into the page), which results from the difference in the magnetic field magnitudes.

The key point is the use of the right-hand rule for each wire, based on the direction of current flow, which determines the direction of the magnetic field at point \( P \).

Would you like more details on this or have further questions? Here are some additional questions to consider:

1. How would the magnetic field at \( P \) change if the currents in both wires were reversed?
2. What would happen if point \( P \) were located to the left of both wires?
3. How does the distance from the wires affect the strength of the magnetic field at point \( P \)?
4. Why does the magnetic field decrease with distance from the wire, and how is it mathematically represented?
5. Could you find a point between the wires where the net magnetic field would be zero?

**Tip:** Using the right-hand rule effectively is essential in visualizing magnetic fields around current-carrying wires.

Can you explain why I1 is out of the page and I2 is into the page?

Explore why currents I1 and I2 produce magnetic fields in opposite directions at a point in space. This physics problem illustrates the right-hand rule to determine magnetic field directions created by parallel current-carrying wires and includes detailed explanations and calculations.

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