An "infinite" wire, whose center is on the y-axis, carries current 1 = 907 A in the negative y- direction. A short straight wire (length L = 73.7 cm), whose center is on the x-axis, carries current /2 = 372 A in the positive x-direction. The end of the short wire closest to the y-axis is d = 2.65 cm away. Find F, the net force in N, exerted by the long wire on the short wire. The sign will indicate if the force is in the positive y-direction or negative y-direction. HINT: You will have to integrate!
An "infinite" wire, whose center is on the y-axis, carries current 1 = 907 A in the negative y- direction. A short straight wire (length L = 73.7 cm), whose center is on the x-axis, carries current /2 = 372 A in the positive x-direction. The end of the short wire closest to the y-axis is d = 2.65 cm away. Find F, the net force in N, exerted by the long wire on the short wire. The sign will indicate if the force is in the positive y-direction or negative y-direction. HINT: You will have to integrate!
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![**Diagram 4 Explanation**
This diagram illustrates two parallel lines with vectors and labeled distances.
- The vertical line on the left represents a current \( I_1 \), indicated by a thick arrow pointing downward.
- Adjacent to this line is a dashed horizontal line labeled \( x \), indicating a directional axis along the horizontal plane.
- On the horizontal line \( x \), there is a horizontal vector labeled \( I_2 \) pointing to the right.
- Distance \( d \) is marked with a double-headed arrow pointing towards the left from point \( L \) to the line carrying current \( I_1 \).
- Distance \( L \) is marked with a double-headed arrow between point \( I_2 \) and the start of the measurement for distance \( d \).
The diagram demonstrates the spatial relationship between two currents, \( I_1 \) and \( I_2 \), along with their respective distances represented as \( d \) and \( L \) along the horizontal axis. This type of illustration is often used in physics to demonstrate magnetic field interactions or force calculations between two parallel currents.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb19a3fe-0e86-40de-9e6a-8c29c197f63b%2F9b96b0e2-8d8e-4d67-b25c-5b42bc541913%2Ff0q2opn_processed.png&w=3840&q=75)
Transcribed Image Text:**Diagram 4 Explanation**
This diagram illustrates two parallel lines with vectors and labeled distances.
- The vertical line on the left represents a current \( I_1 \), indicated by a thick arrow pointing downward.
- Adjacent to this line is a dashed horizontal line labeled \( x \), indicating a directional axis along the horizontal plane.
- On the horizontal line \( x \), there is a horizontal vector labeled \( I_2 \) pointing to the right.
- Distance \( d \) is marked with a double-headed arrow pointing towards the left from point \( L \) to the line carrying current \( I_1 \).
- Distance \( L \) is marked with a double-headed arrow between point \( I_2 \) and the start of the measurement for distance \( d \).
The diagram demonstrates the spatial relationship between two currents, \( I_1 \) and \( I_2 \), along with their respective distances represented as \( d \) and \( L \) along the horizontal axis. This type of illustration is often used in physics to demonstrate magnetic field interactions or force calculations between two parallel currents.
![Refer to diagram 4.
An "infinite" wire, whose center is on the y-axis, carries current \( I_1 = 907 \, \text{A} \) in the negative y-direction. A short straight wire (length \( L = 73.7 \, \text{cm} \)), whose center is on the x-axis, carries current \( I_2 = 372 \, \text{A} \) in the positive x-direction. The end of the short wire closest to the y-axis is \( d = 2.65 \, \text{cm} \) away. Find \( F \), the net force in Newtons, exerted by the long wire on the short wire. The sign will indicate if the force is in the positive y-direction or negative y-direction.
**HINT:** You will have to integrate!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb19a3fe-0e86-40de-9e6a-8c29c197f63b%2F9b96b0e2-8d8e-4d67-b25c-5b42bc541913%2Fi2izxt_processed.png&w=3840&q=75)
Transcribed Image Text:Refer to diagram 4.
An "infinite" wire, whose center is on the y-axis, carries current \( I_1 = 907 \, \text{A} \) in the negative y-direction. A short straight wire (length \( L = 73.7 \, \text{cm} \)), whose center is on the x-axis, carries current \( I_2 = 372 \, \text{A} \) in the positive x-direction. The end of the short wire closest to the y-axis is \( d = 2.65 \, \text{cm} \) away. Find \( F \), the net force in Newtons, exerted by the long wire on the short wire. The sign will indicate if the force is in the positive y-direction or negative y-direction.
**HINT:** You will have to integrate!
Expert Solution
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Step 1
Consider an element of the short wire at a distance l from the infinite wire.
Force on the short wire due to the element dl
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