The Resultant Magnetic Field at point ‘P’

The resultant magnetic field at point ‘P’ situated midway between two parallel wires (placed horizontally) each carrying a steady current I is

Options:

1. in the same direction as the current in the wires.
2. in the vertically upward direction.
3. zero
4. in the vertically downward direction.

To analyze the figure, we need to understand the principles of magnetism in current-carrying wires. Here’s the breakdown:

Understanding the Setup:

• Two Parallel Wires: The image shows two long, straight wires running parallel to each other.
• Current I: Both wires carry an equal steady current, I, flowing in the same direction (let’s consider to the right, as indicated by points A and B).
• Point P: A point, P, is located exactly midway between the wires.

Understanding the principles:

• Right-hand Thumb Rule: If you point your right-hand thumb in the direction of the current flow in a wire, the curl of your fingers represents the direction of the magnetic field around the wire.
• Magnetic Field at a Point Due to a Straight Wire: The magnetic field at a point near a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.
• Superposition of Magnetic Fields: The total magnetic field at a point due to multiple current-carrying wires is the vector sum of the individual fields created by each wire.

Magnetic Field Analysis:

• Right-Hand Rule: To determine the direction of the magnetic field generated by a current-carrying wire, we use the right-hand rule. If you point your right thumb in the direction of the current, the curl of your fingers indicates the direction of the magnetic field lines, which circle the wire.
• Wire A: The current in Wire A is flowing out of the page (away from you). Using the right-hand thumb rule, the magnetic field around Wire A at point P will be in a clockwise direction.
• Wire B: The current in Wire B is flowing into the page (towards you). The magnetic field around Wire B at point P will be in a counterclockwise direction.
• Superposition Principle: The total magnetic field at a point is the vector sum of the magnetic fields generated by each individual source.
• Resultant Magnetic Field: Since point P is exactly in the middle between the two wires, the magnetic fields from Wire A and Wire B will have the same magnitude. As they are in opposite directions, they will cancel each other out.

Why Option (c) is Correct

• Zero Magnetic Field at P: Because the magnetic fields from the two wires are equal in magnitude and exactly opposite in direction at point P, they cancel each other out. The resultant magnetic field at point P is zero.