Understanding Magnetic Force on a Moving Charge

Let's analyze the force experienced by a positive charge moving in a magnetic field. The force on a charge moving in a magnetic field is called the magnetic force, and it is described by the Lorentz force formula.

The formula for the magnetic force \(\vec{F}\) on a charge \(q\) moving with velocity \(\vec{v}\) in a magnetic field \(\vec{B}\) is given by:

\(\vec{F} = q(\vec{v} \times \vec{B})\)

Here, the charge \(q\) is positive. The direction of the magnetic force \(\vec{F}\) is the same as the direction of the cross product \(\vec{v} \times \vec{B}\).

Analyzing the Directions

We are given the following directions:

• Velocity of the charge (\(\vec{v}\)): Towards South
• Magnetic field (\(\vec{B}\)): Towards North

Consider the directions North and South. These directions are opposite to each other.

Calculating the Cross Product \(\vec{v} \times \vec{B}\)

The magnitude of the cross product \(\vec{v} \times \vec{B}\) is given by \(|\vec{v}| |\vec{B}| \sin(\theta)\), where \(\theta\) is the angle between the velocity vector \(\vec{v}\) and the magnetic field vector \(\vec{B}\).

In this case, the velocity is South and the magnetic field is North. These two directions are exactly opposite.

Therefore, the angle \(\theta\) between \(\vec{v}\) and \(\vec{B}\) is \(180^\circ\).

Now, let's find the value of \(\sin(\theta)\) for \(\theta = 180^\circ\):

\(\sin(180^\circ) = 0\)

The magnitude of the cross product \(\vec{v} \times \vec{B}\) is \(|\vec{v}| |\vec{B}| \sin(180^\circ) = |\vec{v}| |\vec{B}| \times 0 = 0\).

Since the magnitude of the cross product is zero, the vector \(\vec{v} \times \vec{B}\) is the zero vector.

Determining the Magnetic Force

Using the Lorentz force formula:

\(\vec{F} = q(\vec{v} \times \vec{B})\)

Since \(\vec{v} \times \vec{B} = 0\), we have:

\(\vec{F} = q(0) = 0\)

The magnetic force on the charge is zero.

A zero force means that the charge will not be deflected from its path by the magnetic field.

Conclusion on Deflecting Force

The moving positive charge experiences no deflecting force when its velocity is parallel or anti-parallel to the magnetic field direction.

In this specific scenario, the velocity (South) is anti-parallel to the magnetic field (North), resulting in no magnetic force and thus, no deflection.

Based on our analysis, the charge will experience no deflecting force.

Summary of Options Analysis

• Option 1: a deflecting force towards north direction. (Incorrect, force is zero)
• Option 2: a deflecting force towards east direction. (Incorrect, force is zero)
• Option 3: a deflecting force towards west direction. (Incorrect, force is zero)
• Option 4: no deflecting force. (Correct, force is zero)

Revision Table: Magnetic Force Concepts

Additional Information: Magnetic Force Direction

While not needed when the force is zero, the direction of the magnetic force on a positive charge can be found using the Right-Hand Rule for cross products or specific magnetic force rules:

• Right-Hand Rule (Cross Product): Point the fingers of your right hand in the direction of the first vector (\(\vec{v}\)), curl them towards the direction of the second vector (\(\vec{B}\)). Your thumb points in the direction of the cross product (\(\vec{v} \times \vec{B}\)). For a positive charge, this is the direction of the force.
• Right-Hand Rule (for Positive Charge): Point your thumb in the direction of the velocity (\(\vec{v}\)), your fingers in the direction of the magnetic field (\(\vec{B}\)). The palm of your hand faces in the direction of the magnetic force (\(\vec{F}\)).

If the charge is negative, the direction of the force is opposite to the direction given by these rules.

In our problem, since \(\vec{v}\) and \(\vec{B}\) are anti-parallel (South and North), \(\sin(180^\circ)\) is 0, leading to zero force regardless of using any rule, as the magnitude itself is zero.