A positively charged particle projected towards east is deflected towards north by a magnetic field. The field may be

Options

A. towards west
B. towards south
C. upward
D. downward

Answer

To solve the problem, we need to determine the direction of the magnetic field given the motion of a positively charged particle and the direction of the force acting on it.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- A positively charged particle is projected towards the east.
- The particle is deflected towards the north due to a magnetic field.

2. **Understand the Forces Involved:**
- The magnetic force acting on a charged particle is given by the equation:
\[ \vec{F} = q (\vec{v} \times \vec{B}) \]
where:
- \( \vec{F} \) is the magnetic force,
- \( q \) is the charge of the particle,
- \( \vec{v} \) is the velocity vector of the particle,
- \( \vec{B} \) is the magnetic field vector.

3. **Determine the Direction of the Velocity Vector (\( \vec{v} \)):**
- Since the particle is projected towards the east, we can represent the velocity vector \( \vec{v} \) pointing to the right (east).

4. **Determine the Direction of the Force Vector (\( \vec{F} \)):**
- The particle is deflected towards the north, which means the magnetic force \( \vec{F} \) is directed upwards (north).

5. **Use the Right-Hand Rule:**
- To find the direction of the magnetic field \( \vec{B} \), we can use the right-hand rule for the cross product:
- Point your right thumb in the direction of the velocity vector \( \vec{v} \) (east).
- Point your fingers in the direction of the force vector \( \vec{F} \) (north).
- Your palm will then face in the direction of the magnetic field \( \vec{B} \).

6. **Determine the Direction of the Magnetic Field (\( \vec{B} \)):**
- Following the right-hand rule, if your thumb points east (direction of \( \vec{v} \)) and your fingers point north (direction of \( \vec{F} \)), your palm will face downwards. Thus, the magnetic field \( \vec{B} \) is directed downwards.

### Final Answer:
The magnetic field may be directed downwards.