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

The correct option is Upward.

Explanation

The direction of the magnetic force on a moving charged particle is governed by the Lorentz Force law. For a positively charged particle, the direction of force, magnetic field, and velocity can be determined using Fleming’s Left-Hand Rule.

Detailed Analysis:
According to Fleming’s Left-Hand Rule, the three fingers of the left hand are stretched mutually perpendicular to each other:

• Forefinger: Represents the direction of the Magnetic Field.
• Middle Finger: Represents the direction of the Current (or velocity of a positive charge).
• Thumb: Represents the direction of the Force (or motion).

Applying this to the given scenario:

1. Current (Velocity): The particle is positively charged and moves towards the West. Align the middle finger towards the West.
2. Force (Deflection): The particle is deflected towards the North. Align the thumb towards the North.
3. Magnetic Field: With the middle finger pointing West and the thumb pointing North, the forefinger naturally points Upward (perpendicular to the horizontal plane defined by North and West).

Vector Verification:
Mathematically, the force vector $\vec{F}$ is given by the cross product $\vec{F} = q(\vec{v} \times \vec{B})$.

• Let West be $-\hat{i}$ and North be $+\hat{j}$.
• We require $(-\hat{i}) \times \vec{B} = \hat{j}$.
• Using the cross product rule $\hat{i} \times \hat{k} = -\hat{j}$, it follows that $(-\hat{i}) \times \hat{k} = \hat{j}$.
• Therefore, the direction of the magnetic field $\vec{B}$ corresponds to $+\hat{k}$, which is the Upward direction.

Key Takeaway:
A magnetic force is always perpendicular to both the velocity of the charge and the magnetic field. The direction for positive charges is found using Fleming's Left-Hand Rule or the Right-Hand Palm Rule.