If the direction of the initial velocity of the charged particle is perpendicular to the magnetic field, then the orbit will be

Options

A. A straight line
B. An ellipse
C. A circle
D. A helix

Answer

To solve the question, "If the direction of the initial velocity of the charged particle is perpendicular to the magnetic field, then the orbit will be:", we can follow these steps:

### Step 1: Understand the scenario
We have a charged particle moving in a magnetic field. The direction of the initial velocity of this charged particle is perpendicular to the direction of the magnetic field.

**Hint:** Visualize the setup: draw the magnetic field lines and the velocity vector of the charged particle.

### Step 2: Apply the Lorentz Force Law
The force acting on a charged particle moving in a magnetic field is given by the Lorentz force equation:
\[ \vec{F} = q (\vec{v} \times \vec{B}) \]
where \( q \) is the charge of the particle, \( \vec{v} \) is the velocity vector, and \( \vec{B} \) is the magnetic field vector.

**Hint:** Remember that the cross product results in a force that is perpendicular to both the velocity and the magnetic field.

### Step 3: Determine the nature of the motion
Since the velocity of the charged particle is perpendicular to the magnetic field, the magnetic force will also be perpendicular to the velocity. This means that the force does not do work on the particle (as work is force in the direction of displacement), and thus the speed of the particle remains constant.

**Hint:** Think about how forces acting perpendicular to the motion affect the trajectory of the particle.

### Step 4: Identify the resulting path
When a force acts perpendicular to the velocity of an object, it causes the object to move in a circular path. The magnetic force acts as a centripetal force, pulling the particle towards the center of the circular path.

**Hint:** Recall the conditions for circular motion: a constant speed and a force directed towards the center of the circular path.

### Step 5: Conclusion
Since the charged particle moves in a circular path due to the constant perpendicular magnetic force, we conclude that if the initial velocity of the charged particle is perpendicular to the magnetic field, the orbit will be circular.

**Final Answer:** The orbit will be a circle.