||| INT A 20-cm-long, zero-resistance wire is pulled outward, on zero-resistance rail: a steady speed of 10 m/s in a 0.10 T magnetic field. (See Figure P25.630.) On the opp side, a 1.0 carbon resistor completes the circuit by connecting the two rails. The ma the resistor is 50 mg. a. What is the induced current in the circuit? b. How much force is needed to pull the wire at this speed? c- Calculate the power dissipation in the resistor.

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Chapter1: Units, Trigonometry. And Vectors
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### Problem Description

A 20-cm-long, zero-resistance wire is pulled outward, on zero-resistance rails, at a steady speed of 10 m/s in a 0.10 T magnetic field. On the opposite side, a 1.0 Ω carbon resistor completes the circuit by connecting the two rails. The mass of the resistor is 50 mg.

**Questions:**
- **a.** What is the induced current in the circuit?
- **b.** How much force is needed to pull the wire at this speed?
- **c.** Calculate the power dissipation in the resistor.

### Diagram Explanation

The diagram shows:

- A rectangular loop with a horizontal top and bottom, and a movable vertical wire on one side.
- Lines with "×" marks indicate a magnetic field directed into the page.
- The length of the wire is indicated as \( l = 20 \, \text{cm} \).
- The magnetic field strength is \( 0.1 \, \text{T} \).
- The movable wire is being pulled at a velocity \( v = 10 \, \text{m/s} \).
- A \( 1.0 \, \Omega \) resistor is connected on the opposite side of the loop, completing the circuit.
- The setup is free of any intrinsic electrical resistance other than the given resistor.
Transcribed Image Text:### Problem Description A 20-cm-long, zero-resistance wire is pulled outward, on zero-resistance rails, at a steady speed of 10 m/s in a 0.10 T magnetic field. On the opposite side, a 1.0 Ω carbon resistor completes the circuit by connecting the two rails. The mass of the resistor is 50 mg. **Questions:** - **a.** What is the induced current in the circuit? - **b.** How much force is needed to pull the wire at this speed? - **c.** Calculate the power dissipation in the resistor. ### Diagram Explanation The diagram shows: - A rectangular loop with a horizontal top and bottom, and a movable vertical wire on one side. - Lines with "×" marks indicate a magnetic field directed into the page. - The length of the wire is indicated as \( l = 20 \, \text{cm} \). - The magnetic field strength is \( 0.1 \, \text{T} \). - The movable wire is being pulled at a velocity \( v = 10 \, \text{m/s} \). - A \( 1.0 \, \Omega \) resistor is connected on the opposite side of the loop, completing the circuit. - The setup is free of any intrinsic electrical resistance other than the given resistor.
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