1. A 0.80-m aluminum bar is held with its length parallel to the east- west direction and dropped from a bridge. Just before the bar hits the river below, its speed is 22 m/s, and the emf induced across its length is 6.5 x 10-4 V. Assuming the horizontal component of the earth's mag- netic field at the location of the bar points directly north, (a) determine the magnitude of the horizontal component of the earth's magnetic field, and (b) state whether the east end or the west end of the bar is positive.
1. A 0.80-m aluminum bar is held with its length parallel to the east- west direction and dropped from a bridge. Just before the bar hits the river below, its speed is 22 m/s, and the emf induced across its length is 6.5 x 10-4 V. Assuming the horizontal component of the earth's mag- netic field at the location of the bar points directly north, (a) determine the magnitude of the horizontal component of the earth's magnetic field, and (b) state whether the east end or the west end of the bar is positive.
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![**Problem Statement:**
1. A 0.80-m aluminum bar is held with its length parallel to the east-west direction and dropped from a bridge. Just before the bar hits the river below, its speed is 22 m/s, and the emf induced across its length is 6.5 × 10^-4 V. Assuming the horizontal component of the earth’s magnetic field at the location of the bar points directly north,
(a) determine the magnitude of the horizontal component of the earth’s magnetic field, and
(b) state whether the east end or the west end of the bar is positive.
**Instructions for Student:**
Your task is to utilize the provided information to solve the following sub-questions:
### (a) Determining the Magnitude of the Horizontal Component of Earth's Magnetic Field
To find the magnitude of the horizontal component of the Earth's magnetic field, \( B \), we can use the formula for the electromotive force (emf) induced in a moving conductor:
\[ \text{emf} = B \cdot v \cdot l \]
Where:
- \(\text{emf}\) = 6.5 × 10^-4 V
- \( v \) = 22 m/s
- \( l \) = 0.80 m
Rearrange the formula to solve for \( B \):
\[ B = \frac{\text{emf}}{v \cdot l} \]
Plug in the values:
\[ B = \frac{6.5 \times 10^{-4} \text{ V}}{22 \text{ m/s} \times 0.80 \text{ m}} \]
Perform the calculation to determine the magnitude of \( B \).
### (b) Determining the Positive End of the Bar
To determine whether the east end or the west end of the bar is positive, we need to consider the direction of the induced current due to the motion of the bar through the Earth's magnetic field. According to the right-hand rule for generators, if the thumb points in the direction of the velocity (west) and the fingers point in the direction of the magnetic field (north), the palm faces the direction of the induced conventional current, and the direction pointed by the palm is the positive end of the bar.
Reflect on the setup and deduce which end of the bar (east or west) becomes positive based on the right](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc02bfde4-a78d-4551-93f6-03d589a5c8dc%2F3826c110-66bd-4d4d-ab7a-46738d7b1e38%2Fn385vyy_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
1. A 0.80-m aluminum bar is held with its length parallel to the east-west direction and dropped from a bridge. Just before the bar hits the river below, its speed is 22 m/s, and the emf induced across its length is 6.5 × 10^-4 V. Assuming the horizontal component of the earth’s magnetic field at the location of the bar points directly north,
(a) determine the magnitude of the horizontal component of the earth’s magnetic field, and
(b) state whether the east end or the west end of the bar is positive.
**Instructions for Student:**
Your task is to utilize the provided information to solve the following sub-questions:
### (a) Determining the Magnitude of the Horizontal Component of Earth's Magnetic Field
To find the magnitude of the horizontal component of the Earth's magnetic field, \( B \), we can use the formula for the electromotive force (emf) induced in a moving conductor:
\[ \text{emf} = B \cdot v \cdot l \]
Where:
- \(\text{emf}\) = 6.5 × 10^-4 V
- \( v \) = 22 m/s
- \( l \) = 0.80 m
Rearrange the formula to solve for \( B \):
\[ B = \frac{\text{emf}}{v \cdot l} \]
Plug in the values:
\[ B = \frac{6.5 \times 10^{-4} \text{ V}}{22 \text{ m/s} \times 0.80 \text{ m}} \]
Perform the calculation to determine the magnitude of \( B \).
### (b) Determining the Positive End of the Bar
To determine whether the east end or the west end of the bar is positive, we need to consider the direction of the induced current due to the motion of the bar through the Earth's magnetic field. According to the right-hand rule for generators, if the thumb points in the direction of the velocity (west) and the fingers point in the direction of the magnetic field (north), the palm faces the direction of the induced conventional current, and the direction pointed by the palm is the positive end of the bar.
Reflect on the setup and deduce which end of the bar (east or west) becomes positive based on the right
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