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.
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!
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
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

F=I2dl×B1=I2dli^×μ0I12πlk^=μ0I1I22πldl-j^

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