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vecF is the force on the arm of a square...

`vecF` is the force on the arm of a square toop suspended in a uniform mdgnetic field. Net : force on remaining arnis is :

A

`- vecF`

B

`vecF`

C

`-3 vecF`

D

`3 vecF`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the forces acting on the arms of a square loop suspended in a uniform magnetic field. ### Step-by-Step Solution: 1. **Understanding the Setup**: - We have a square loop suspended in a uniform magnetic field. - The loop carries a current, which interacts with the magnetic field to produce forces on the arms of the loop. 2. **Identifying the Forces**: - The magnetic force on a current-carrying conductor in a magnetic field is given by the formula: \[ \vec{F} = I (\vec{L} \times \vec{B}) \] where \(I\) is the current, \(\vec{L}\) is the length vector of the conductor, and \(\vec{B}\) is the magnetic field. 3. **Analyzing the Arms Parallel to the Field**: - For the two arms of the loop that are parallel to the magnetic field, the angle between the current direction and the magnetic field is 0 degrees. - Therefore, the force on these arms is: \[ \vec{F}_{\text{parallel}} = I (\vec{L} \times \vec{B}) = 0 \] This is because the cross product of two parallel vectors is zero. 4. **Analyzing the Remaining Arms**: - The other two arms of the square loop are perpendicular to the magnetic field. - The force on these arms can be calculated using the same formula. Since the angle is 90 degrees, the force will be: \[ \vec{F}_{\text{perpendicular}} = I L B \] - If we denote the force on one of these arms as \(\vec{F}\), then the force on the other arm will be equal in magnitude but opposite in direction. 5. **Net Force on the Remaining Arms**: - The total force on the two arms that are perpendicular to the magnetic field will be: \[ \vec{F}_{\text{net}} = \vec{F} + (-\vec{F}) = 0 \] - However, since we are interested in the net force on the remaining arms, we can express it as: \[ \text{Net force on remaining arms} = -\vec{F} \] 6. **Conclusion**: - The net force on the remaining arms of the square loop is given by: \[ \text{Net force on remaining arms} = -\vec{F} \] ### Final Answer: The net force on the remaining arms is \(-\vec{F}\).

To solve the problem, we need to analyze the forces acting on the arms of a square loop suspended in a uniform magnetic field. ### Step-by-Step Solution: 1. **Understanding the Setup**: - We have a square loop suspended in a uniform magnetic field. - The loop carries a current, which interacts with the magnetic field to produce forces on the arms of the loop. ...
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