A positively charged particle projected towards west is deflected towards north by a magnetic field. The direction of the magnetic field is

Options

A. towards south
B. towards east
C. in downward direction
D. in upward direction

Explanation

To determine the direction of the magnetic field when a positively charged particle is projected towards the west and is deflected towards the north, we can use the right-hand rule for the magnetic force on a charged particle. Here’s a step-by-step solution:

### Step 1: Identify the directions
- The positively charged particle is moving towards the west.
- The particle is deflected towards the north.

### Step 2: Use the right-hand rule
- According to the right-hand rule, if you point your thumb in the direction of the velocity of the charged particle (west), and your fingers in the direction of the magnetic field (which we need to determine), then your palm will face in the direction of the magnetic force acting on the particle.

### Step 3: Assign directions
- Let’s denote:
- West as the negative x-direction.
- North as the positive y-direction.
- Upward (out of the plane) as the positive z-direction.

### Step 4: Apply the right-hand rule
- Point your thumb to the west (negative x-direction).
- The force on the positively charged particle is directed north (positive y-direction).
- To find the direction of the magnetic field, we need to orient our fingers so that when we curl them from the velocity (west) to the force (north), our palm faces the direction of the force.

### Step 5: Determine the magnetic field direction
- If your thumb points west and your palm faces north, your fingers must curl upwards. This indicates that the magnetic field is directed upwards (positive z-direction).

### Conclusion
- Therefore, the direction of the magnetic field is **upward** (or out of the plane).