### Problem Description: Moving Copper Rod in Magnetic FieldA thin 0.120 m copper rod on the \( x \)-\( y \) plane and parallel to the \( x \)-axis moves with a constant velocity of 4.17 m/s in the \( +y \) direction, as shown in the figure below. There is a uniform magnetic field of 0.0584 T everywhere in space pointing in the \( -z \) direction (into the page). The electric potential is measured to be \( V_a \) at point \( a \) and \( V_b \) at point \( b \). What is the potential difference \( V_a - V_b \)? (Make sure to write down the sign and magnitude).#### Diagram Explanation:- The diagram features a horizontal rod on the \( x \)-\( y \) plane, indicated as black line.- The \( y \)-axis is marked with positive values upwards (\( +y \)).- The \( x \)-axis is marked with positive values to the right (\( +x \)).- The magnetic field (\( B \)) is shown to be directed into the page, represented symbolically with a circle and a cross (\( +z \)).- Points \( a \) and \( b \) are labeled on the rod, with point \( a \) on the right side and point \( b \) on the left side.- The velocity vector (\( v \)) is shown pointing upwards along the \( +y \)-axis.#### Given Data:- Length of the rod (\( L \)) = 0.120 m- Velocity (\( v \)) = 4.17 m/s in the \( +y \) direction- Magnetic field (\( B \)) = 0.0584 T, in the \( -z \) direction (into the page)- Electric potentials: \( V_a \) at point \( a \) and \( V_b \) at point \( b \)#### Objective:Calculate the potential difference \( V_a - V_b \).### Solution:The potential difference induced in the rod moving through the magnetic field can be calculated using the formula for motional emf (electromotive force):\[ \mathcal{E} = vBL \]Where:- \( v \) is the velocity- \( B \) is the magnetic field strength- \( L \) is the

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(L11) A thin 0.120 m copper rod on the x-y plane and parallel to the x axis moves with a constant velocity of 4.17 m/s in the +y direction as shown in the figure. There is a uniform magnetic field 5.84E-2 T everywhere in space pointing in the −z direction (into the page). The electric potential is measured to be Va at point a and V at point b. What is the potential difference Va-Vb (write down the sign and magnitude)? +y +zO Vb Va +x

(L11) A thin 0.120 m copper rod on the x-y plane and parallel to the x axis moves with a constant velocity of 4.17 m/s in the +y direction as shown in the figure. There is a uniform magnetic field 5.84E-2 T everywhere in space pointing in the −z direction (into the page). The electric potential is measured to be Va at point a and V at point b. What is the potential difference Va-Vb (write down the sign and magnitude)? +y +zO Vb Va +x

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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Concept explainers

Ferromagnetism

Ferromagnetism is a mechanism by which some materials show magnetic properties. Iron and magnetite, an oxide of iron, are two naturally occurring materials that show the property of ferromagnetism. The word ferromagnetism is derived from the Latin name of iron, "Ferrum" as it was the first observed material to show such property. The property of ferromagnetism is shown by only a few substances such as iron, nickel, cobalt, and their alloys. Some transition metals and alloys of rare-earth metals also show ferromagnetism.

Question

### Problem Description: Moving Copper Rod in Magnetic Field

A thin 0.120 m copper rod on the \( x \)-\( y \) plane and parallel to the \( x \)-axis moves with a constant velocity of 4.17 m/s in the \( +y \) direction, as shown in the figure below. There is a uniform magnetic field of 0.0584 T everywhere in space pointing in the \( -z \) direction (into the page). The electric potential is measured to be \( V_a \) at point \( a \) and \( V_b \) at point \( b \). What is the potential difference \( V_a - V_b \)? (Make sure to write down the sign and magnitude).

#### Diagram Explanation:
- The diagram features a horizontal rod on the \( x \)-\( y \) plane, indicated as black line.
- The \( y \)-axis is marked with positive values upwards (\( +y \)).
- The \( x \)-axis is marked with positive values to the right (\( +x \)).
- The magnetic field (\( B \)) is shown to be directed into the page, represented symbolically with a circle and a cross (\( +z \)).
- Points \( a \) and \( b \) are labeled on the rod, with point \( a \) on the right side and point \( b \) on the left side.
- The velocity vector (\( v \)) is shown pointing upwards along the \( +y \)-axis.

#### Given Data:
- Length of the rod (\( L \)) = 0.120 m
- Velocity (\( v \)) = 4.17 m/s in the \( +y \) direction
- Magnetic field (\( B \)) = 0.0584 T, in the \( -z \) direction (into the page)
- Electric potentials: \( V_a \) at point \( a \) and \( V_b \) at point \( b \)

#### Objective:
Calculate the potential difference \( V_a - V_b \).

### Solution:

The potential difference induced in the rod moving through the magnetic field can be calculated using the formula for motional emf (electromotive force):
\[ \mathcal{E} = vBL \]

Where:
- \( v \) is the velocity
- \( B \) is the magnetic field strength
- \( L \) is the

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