Current flows through uniform square frames as shown. In which case is the magnetic field at the centre of the frame not zero ?

Options

A.
B.
C.
D.

Explanation

To determine in which case the magnetic field at the center of a uniform square frame is not zero, we will analyze each option using the right-hand thumb rule. This rule helps us find the direction of the magnetic field produced by a current-carrying conductor.

### Step-by-Step Solution:

1. **Understanding the Right-Hand Thumb Rule**:
- The right-hand thumb rule states that if you point your thumb in the direction of the current, the curl of your fingers will indicate the direction of the magnetic field lines around the conductor.

2. **Analyzing Each Option**:
- We will consider the current direction in each section of the square frame and determine the resultant magnetic field at the center.

3. **Option 1**:
- In this option, the current enters one junction and exits another.
- For the sections:
- **Section 1**: Current flowing inwards (magnetic field directed into the center).
- **Section 3**: Current flowing outwards (magnetic field directed out of the center).
- The magnetic fields from sections 1 and 3 cancel each other out, resulting in zero net magnetic field.
- **Sections 2 and 4**: Both have outward magnetic fields, which add up.
- Therefore, the net magnetic field at the center is **non-zero**.

4. **Option 2**:
- Similar to option 1, the current flows in such a way that:
- **Sections 1 and 3**: Cancel each other out.
- **Sections 2 and 4**: Both have outward magnetic fields, which add up.
- Thus, the net magnetic field at the center is also **non-zero**.

5. **Option 3**:
- Current flows in a manner where:
- **Sections 1 and 3**: Magnetic fields cancel each other out.
- **Sections 2 and 4**: Magnetic fields also cancel each other out.
- Therefore, the net magnetic field at the center is **zero**.

6. **Option 4**:
- The current flows in such a way that:
- **Sections 1 and 3**: Magnetic fields cancel each other out.
- **Sections 2 and 4**: Magnetic fields also cancel each other out.
- Thus, the net magnetic field at the center is **zero**.

### Conclusion:
The magnetic field at the center of the frame is **not zero** in **Option 1 and Option 2**.