A positively charged particle moving due east enters a region of uniform magnetic field directed vertically upwards. The partical will be

Options

A. conitinue to move due east
B. move in a circular orbit with its speed unchanged
C. move in a circular orbit with its speed increased
D. gets deflected vertically upwards

Answer

To solve the problem, we need to analyze the motion of a positively charged particle moving in a magnetic field. Here’s a step-by-step solution:

### Step 1: Identify the Directions
- The positively charged particle is moving due east.
- The magnetic field is directed vertically upwards.

### Step 2: Use the Right-Hand Rule
- To determine the direction of the force acting on the charged particle, we can use the right-hand rule for the cross product \( \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \).
- Point your fingers in the direction of the velocity (\( \mathbf{v} \), which is east) and curl them towards the direction of the magnetic field (\( \mathbf{B} \), which is upwards).

### Step 3: Determine the Force Direction
- When you apply the right-hand rule, your thumb will point in the direction of the magnetic force (\( \mathbf{F} \)).
- In this case, the thumb will point towards the south, indicating that the force acting on the particle is directed southward.

### Step 4: Analyze the Motion
- Since the magnetic force is perpendicular to the velocity of the particle, it will not change the speed of the particle but will change its direction.
- Therefore, the particle will start to move in a circular path due to the continuous change in direction caused by the magnetic force.

### Step 5: Conclusion
- The particle will move in a circular orbit with its speed unchanged. This is because the magnetic force does not do work on the particle (as it is always perpendicular to the velocity), and thus the kinetic energy (and speed) remains constant.

### Final Answer
The correct option is: **Move in a circular orbit with speed unchanged.**

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