Moving Charges and Magnetism

Introduction

Since the beginning, magnets have been an integral part of our childhood. It was quite surprising how a bar magnet could grab so many iron nails. The magnet has the property to repel or attract other substances, referred to as Magnetism. When two bar magnets are positioned close to one another, the same poles will repel each other; however, the opposite poles will attract. The primary reason behind this behavior of the magnet is the imaginary magnetic line that continuously revolves around. Similar to the electrostatic force and the gravitational force, it is also an interaction from a distance. 

Hans Christian Oersted made an observation which later proved as a discovery indicating the relationship between electricity and magnetism. While performing experiments, he observed that the magnet gets deflected if kept near wires carrying current. 

His work illustrated that one way to produce magnetic effects is by moving electrical charges. One of the branches of Physics that talks about magnetism due to the electric current is known as electromagnetism. 

What is an Electric Field? 

The electric field can be defined as when a single charged particle can exert force to the extent that other non-charged particles can feel its force. This is often termed the Electric field. The electric field is a vector meaning it consists of both directions and the magnitude. Lines of force are differentiated based on positively or negatively charged particles. If it is positively charged, the force line will be directed outwards; however, it will be directed inwards for a negative charge. 

Moving charge force in a magnetic field

Do you know the mechanism through which the magnet employed the force on another? The fact is that current is the reason behind all magnetism. Moving charge forces are exerted in a magnetic field, and due to which the forces are exerted on magnets most of which includes moving charges. Learn in detail about the force on a moving charge in a magnetic field.

One of the most known facts is the magnetic force onto the moving charge. Magnetic force on a moving charge is very important as the Coulomb or electrostatic force, however, it is more dynamic in both its direction and factors affecting it. The magnetic force of magnitude F on a moving charge q at speed donated by v in the magnetic field B is denoted by

 F = qvB sin θ

Here, the angle between two directions (v and B) is donated by θ which is known as Lorentz force. Tesla (T) is the SI unit for magnetic fields. 

A smaller unit, Gauss (G) – 

1 G = 10−4 T, is used sometimes. 

The magnetic field of Earth on its surface = 5 × 10−5T or 0.5 G  

According to Rule 1 – Right-hand, the plane developed by B and v is perpendicular to the magnetic force F direction. To analyze the magnetic force direction, the right-hand thumb should be pointed towards v and the fingers should be placed to B. Several field lines and fingers are representing them. In the direction we push our palm in, the force is in a similar direction. The force on the negative charge is exactly placed opposite to the positive charge. 

1. Case1: – When particles are rotating perpendicular to the circular path

When the magnetic field B is perpendicular to the charged particles velocity v then 

The force will reach its maximum potential( =qvB). Hence, the path will appear circular. Note, in a circle, the velocity with radius and tangent always remains perpendicular to one another.

2. Case 2:- Helical path appears at the time when the charged particles move at a field angle 

Imagine q, a charged particle enters with velocity v to a magnetic field donated by B at an angle θ. Its direction is given as B and velocity as v 

•  The Velocity with field direction which means X-axis, Vx = vcosθ. The component which is parallel remains unaffected due to the magnetic field. Therefore, the particles that are charged continues to revolve in the field at a speed of vcosθ
•  The v component is perpendicular to the field direction along the Y- axis, vy= vsinθ. 

Because of this velocity component, a force F= qvBsinθ is experienced by the charged particles, acting perpendicular to B and vsinθ.

The radius here is,  

These charged particles move a uniform magnetic field. It has 2 concurrent motions including: 

•  a linear motion placed along the X-axis in the B direction

•  a circular motion along a plane which is placed perpendicularly to the Y-Z plane 

Conclusion

Till now we discussed the moving charges and magnetism, magnetic force in detail. The magnetic field exerts a force on q which is the moving charge. The electric field is a vector meaning it consists of both directions and the magnitude. Lines of force are differentiated based on positively or negatively charged particles. We hope this topic is clear.