A vertical straight conductor carries a current vertically upwards. A point `P` lies to the east of it at a small distance and another point `Q` lies to the west at the same distance. The magnetic field at `P` is

Options

A. Greater than at Q
B. Same as at Q
C. Less than at Q
D. Greater or less than at Q depending upon the magnetic field strength

Answer

To solve the problem, we need to determine the magnetic field at point P, which is located to the east of a vertical straight conductor carrying current upwards, and compare it to the magnetic field at point Q, which is located to the west of the same conductor.

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a vertical straight conductor carrying a current \( I \) in the upward direction.
- Point \( P \) is located to the east of the conductor, and point \( Q \) is located to the west, both at the same distance \( R \) from the conductor.

2. **Use the Right-Hand Rule**:
- To determine the direction of the magnetic field created by the current in the conductor, we can use the right-hand rule.
- Point your thumb in the direction of the current (upwards), and curl your fingers around the conductor. Your fingers will point in the direction of the magnetic field lines.

3. **Determine the Magnetic Field at Point P**:
- At point \( P \) (to the east), the magnetic field \( B_P \) will be directed into the page (or screen) based on the right-hand rule.

4. **Determine the Magnetic Field at Point Q**:
- At point \( Q \) (to the west), the magnetic field \( B_Q \) will be directed out of the page (or screen) based on the right-hand rule.

5. **Calculate the Magnitude of the Magnetic Field**:
- The magnitude of the magnetic field due to a long straight conductor at a distance \( R \) is given by the formula:
\[ B = \frac{\mu_0 I}{2 \pi R} \]
- Since both points \( P \) and \( Q \) are at the same distance \( R \) from the conductor, the magnitudes of the magnetic fields at both points will be equal:
\[ B_P = B_Q = \frac{\mu_0 I}{2 \pi R} \]

6. **Conclusion**:
- The magnitudes of the magnetic fields at points \( P \) and \( Q \) are equal, but their directions are opposite. Therefore, we can conclude that:
\[ |B_P| = |B_Q| \]
- The correct option is that the magnetic field at point \( P \) is equal in magnitude to the magnetic field at point \( Q \), but they have opposite directions.