A square current carrying loop is suspended in a unifrom magnetic field acting in the plane of the loop. If the force on one arm of the loop is `vec(F)`, the net force on the remaining three arms of the loop is

Options

A. 3F
B. `-F`
C. `-3F`
D. F

Answer

To solve the problem, let's analyze the situation step by step.

### Step 1: Understand the Configuration
We have a square current-carrying loop suspended in a uniform magnetic field. The magnetic field is acting in the plane of the loop. Let's denote the arms of the loop as A, B, C, and D.

**Hint:** Visualize the square loop and the direction of the magnetic field.

### Step 2: Identify the Force on One Arm
We are given that the force on one arm of the loop (let's say arm A) is \( \vec{F} \). This force is due to the interaction of the magnetic field with the current flowing through that arm.

**Hint:** Recall that the force on a current-carrying conductor in a magnetic field is given by \( \vec{F} = I (\vec{L} \times \vec{B}) \).

### Step 3: Analyze the Forces on the Other Arms
- **Arm B:** The current in this arm is parallel to the magnetic field. According to the Lorentz force law, the force on a current-carrying conductor is zero when the current is parallel to the magnetic field. Therefore, the force on arm B is \( 0 \).

- **Arm C:** The current in this arm flows in the opposite direction to arm A. By applying Fleming's left-hand rule, the force on arm C will be equal in magnitude but opposite in direction to the force on arm A. Thus, the force on arm C is \( -\vec{F} \).

- **Arm D:** Similar to arm B, the current in arm D is also parallel to the magnetic field. Hence, the force on arm D is also \( 0 \).

**Hint:** Remember that forces on arms parallel to the magnetic field are zero.

### Step 4: Calculate the Net Force on the Remaining Three Arms
Now we can sum up the forces on the remaining three arms (B, C, and D):
- Force on arm B = \( 0 \)
- Force on arm C = \( -\vec{F} \)
- Force on arm D = \( 0 \)

Thus, the net force \( \vec{F}_{\text{net}} \) on the remaining three arms is:
\[ \vec{F}_{\text{net}} = 0 + (-\vec{F}) + 0 = -\vec{F} \]

### Final Answer
The net force on the remaining three arms of the loop is \( -\vec{F} \).

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