A charge `+ Q` is moving upwards vertically. It enters a magnetic field directed to the north. The force on the charge will be towards

Options

A. North
B. South
C. East
D. West

Answer

To determine the direction of the force on a charge \( +Q \) moving in a magnetic field, we can use the right-hand rule for the Lorentz force. Here's a step-by-step solution:

### Step 1: Identify the Direction of Motion
The charge \( +Q \) is moving upwards vertically. We can denote this upward direction as the positive \( z \)-axis.

### Step 2: Identify the Direction of the Magnetic Field
The magnetic field is directed to the north. We can denote this direction as the positive \( x \)-axis.

### Step 3: Apply the Right-Hand Rule
According to the Lorentz force law, the force \( \mathbf{F} \) on a charge moving in a magnetic field is given by the equation:
\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]
where:
- \( q \) is the charge,
- \( \mathbf{v} \) is the velocity vector of the charge,
- \( \mathbf{B} \) is the magnetic field vector.

Using the right-hand rule:
- Point your thumb in the direction of the velocity (\( +Q \) moving upwards, so thumb points up).
- Point your fingers in the direction of the magnetic field (north, so fingers point towards the north).

### Step 4: Determine the Direction of the Force
When you apply the right-hand rule:
- Your thumb points up (velocity),
- Your fingers point north (magnetic field),
- Your palm will face towards the west.

Thus, the force on the charge \( +Q \) will be directed towards the west.

### Conclusion
The force on the charge \( +Q \) is directed towards the west.