A wire has a current of 22 A flowing to the left. At a point that is 5 cm above this wire, what is the strength and direction of the magnetic field? 

µ0 = 4π *10^-7

Group of answer choices

2.2* 10^-7 T “into the plane”

2.2* 10^-7 T “out of the plane”

8.8* 10^-5 T “out of the plane”

8.8* 10^-5 T “into the plane”

To determine the strength and direction of the magnetic field at a point above a current-carrying wire, we can use the Biot-Savart law. For a long, straight wire carrying a current \(I\), the magnetic field at a distance \(r\) from the wire is given by:

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

### Given Data:
- Current, \( I = 22 \, \text{A} \)
- Distance from the wire, \( r = 5 \, \text{cm} = 0.05 \, \text{m} \)
- Permeability of free space, \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \)

### Step-by-Step Calculation:

1. **Calculate the magnetic field \(B\)**:
   \[ B = \frac{\mu_0 I}{2 \pi r} \]

2. **Substitute the given values**:
   \[ B = \frac{(4 \pi \times 10^{-7} \, \text{T m/A}) \times 22 \, \text{A}}{2 \pi \times 0.05 \, \text{m}} \]

3. **Simplify the expression**:
   \[ B = \frac{4 \pi \times 10^{-7} \times 22}{2 \pi \times 0.05} \]

4. **Cancel \(\pi\) and simplify further**:
   \[ B = \frac{4 \times 10^{-7} \times 22}{2 \times 0.05} \]
   \[ B = \frac{4 \times 10^{-7} \times 22}{0.1} \]
   \[ B = 4 \times 10^{-6} \times 22 \]
   \[ B = 88 \times 10^{-6} \, \text{T} \]
   \[ B = 8.8 \times 10^{-5} \, \text{T} \]

### Direction of the Magnetic Field:
The direction of the magnetic field around a current-carrying wire can be determined using the right-hand rule. For a current flowing to the left, if you point your thumb in the direction of the current (to the left), your fingers will curl in the direction of the magnetic field.

- **At a point above the wire** (assuming "above" means towards the observer when looking at the wire from above), the magnetic field will point into the plane (or page).

### Correct Answer:
8.8 \(\times\) 10\(^-5\) T “into the plane”

Would you like further details or have any questions? Here are some related questions for further exploration:

1. How does the magnetic field strength change if the distance from the wire is doubled?
2. What would be the magnetic field direction at a point below the wire?
3. How would the magnetic field change if the current direction is reversed?
4. How is the magnetic field affected by a different current magnitude?
5. What is the relationship between magnetic field and electric current in Ampère's law?
6. How does the magnetic field vary in the vicinity of a loop of current?
7. Can the magnetic field due to a straight wire be superimposed with other magnetic fields?
8. What are the practical applications of magnetic fields around current-carrying wires?

**Tip:** Remember to use the right-hand rule consistently when determining the direction of magnetic fields around current-carrying wires.

Learn how to calculate the magnetic field strength and direction above a current-carrying wire. Understand the application of the Biot-Savart law in determining magnetic fields. Solve for 8.8 × 10^-5 T "into the plane". Suitable for advanced high school students studying electromagnetism.

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