Answered: A metal rod is placed on two parallel…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A metal rod is placed on two parallel horizontal conducting rails (see the figure below) in a uniform magnetic field with magnetic flux density B of 1,000 G. The rails are connected with a conducting path with a resistance R of 0.25 Ω. Perpendicular distance between the rails l is 10 cm. Resistance of the rails is negligibly small. The magnetic field is directed vertically down into the ground. The metal rod is moved with a speed v of 5 m/s as shown. Neglect the magnetic field of earth at the location of this apparatus.

Determine:

a.The potential difference between the two rails caused by the motion of the metal rod.

b. Current through the conducting path.

c.Electrical power imparted to the circuit.

d. Direction of current. Explain how you determined this direction.

e. The force required to move the rod.

f.Mechanical power input, using the calculated force and the velocity of the rod.

**Problem Statement:**

6. A metal rod is placed on two parallel horizontal conducting rails (see the figure below) in a uniform magnetic field with magnetic flux density \( B \) of 1,000 G. The rails are connected with a conducting path with a resistance \( R \) of 0.25 Ω. Perpendicular distance between the rails \( l \) is 10 cm. Resistance of the rails is negligibly small. The magnetic field is directed vertically down into the ground. The metal rod is moved with a speed \( v \) of 5 m/s as shown. Neglect the magnetic field of earth at the location of this apparatus.
Determine:
a. The potential difference between the two rails caused by the motion of the metal rod.
b. Current through the conducting path.
c. Electrical power imparted to the circuit.
d. Direction of current. Explain how you determined this direction.
e. The force required to move the rod.
f. Mechanical power input, using the calculated force and the velocity of the rod.

**Diagram Explanation:**

The diagram depicts a horizontal setup where a metal rod is placed on two parallel conducting rails. The magnetic field \( \mathbf{B} \) is shown as pointing vertically into the page (denoted by '×'). The rod, in red, moves perpendicularly across the rails at a velocity \( \mathbf{v} \) of 5 m/s. A resistor \( R \) connects the ends of the rails, forming a closed circuit. The labels in the diagram are as follows:

- **Conducting Rail:** The black vertical lines representing the rails.
- **Metal Rod:** The red horizontal line indicating the rod's position and motion.
- **\( R \):** The resistor connecting the conducting rails.
- **\( l \):** The perpendicular distance between the rails, shown as 10 cm.

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