Refer to diagram 4. An "infinite" horizontal wire lies on the x-axis, and carries current / = 875 A. A short section of wire (length a = 9.28 cm) moves underneath the long wire at constant velocity v = 77.4i m/s. The short wire is perpendicular to the long wire, with the near end distance b = 0.522 cm below. Find the potential difference, in V, induced between the ends of the short wire. You must include the sign: positive means the top of the wire (in the diagram) is higher potential than the bottom; negative means the top of the wire is lower potential than the bottom. HINT: You will have to integrate!

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Refer to diagram 4.

An "infinite" horizontal wire lies on the x-axis and carries a current \( I = 875 \, \text{A} \). A short section of wire (length \( a = 9.28 \, \text{cm} \)) moves underneath the long wire at a constant velocity \( \mathbf{v} = 77.4 \, \text{i m/s} \). The short wire is perpendicular to the long wire, with the near end distance \( b = 0.522 \, \text{cm} \) below. Find the potential difference, in volts, induced between the ends of the short wire. You must include the sign: positive means the top of the wire (in the diagram) is at a higher potential than the bottom; negative means the top of the wire is at a lower potential than the bottom.

**HINT:** You will have to integrate!
Transcribed Image Text:Refer to diagram 4. An "infinite" horizontal wire lies on the x-axis and carries a current \( I = 875 \, \text{A} \). A short section of wire (length \( a = 9.28 \, \text{cm} \)) moves underneath the long wire at a constant velocity \( \mathbf{v} = 77.4 \, \text{i m/s} \). The short wire is perpendicular to the long wire, with the near end distance \( b = 0.522 \, \text{cm} \) below. Find the potential difference, in volts, induced between the ends of the short wire. You must include the sign: positive means the top of the wire (in the diagram) is at a higher potential than the bottom; negative means the top of the wire is at a lower potential than the bottom. **HINT:** You will have to integrate!
### Diagram 4 Explanation

This diagram illustrates a current-carrying wire and the influence of its magnetic field on a moving charge.

#### Description:

- **Horizontal Line (Wire):** The thick horizontal line represents a wire carrying an electric current, denoted by \(I\). The arrow on the wire indicates the direction of the current flow to the right.

- **Vertical Distances:**
  - A perpendicular vertical distance denoted as \(b\) is marked from the wire downward.
  - Below \(b\), another smaller vertical measurement denoted as \(a\) is shown. This represents the vertical positioning of the point of interest relative to the wire.

- **Vertical Bar (Charge):** At the end of distance \(a\), there is a vertical line that might represent a charged particle or object.

- **Arrow (Velocity):** A horizontal arrow labeled \(v\) points to the right from the vertical bar, indicating the direction of the velocity of the charge or object.

This diagram is relevant for understanding concepts such as the magnetic force on a moving charged particle in the vicinity of a current-carrying wire, incorporating principles from electromagnetism, such as Ampère's Law and the Biot-Savart Law.
Transcribed Image Text:### Diagram 4 Explanation This diagram illustrates a current-carrying wire and the influence of its magnetic field on a moving charge. #### Description: - **Horizontal Line (Wire):** The thick horizontal line represents a wire carrying an electric current, denoted by \(I\). The arrow on the wire indicates the direction of the current flow to the right. - **Vertical Distances:** - A perpendicular vertical distance denoted as \(b\) is marked from the wire downward. - Below \(b\), another smaller vertical measurement denoted as \(a\) is shown. This represents the vertical positioning of the point of interest relative to the wire. - **Vertical Bar (Charge):** At the end of distance \(a\), there is a vertical line that might represent a charged particle or object. - **Arrow (Velocity):** A horizontal arrow labeled \(v\) points to the right from the vertical bar, indicating the direction of the velocity of the charge or object. This diagram is relevant for understanding concepts such as the magnetic force on a moving charged particle in the vicinity of a current-carrying wire, incorporating principles from electromagnetism, such as Ampère's Law and the Biot-Savart Law.
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