Charge in Magnetic Field

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Hand Rules Explained

Before we continue it's an important to learn the hand rules that are used in studying electromagnetism.
Hand rules are 'tool's used to establish the correct relationship between the vectors  of electrical current, force, EMF and magnetic field.
There are two in predominant use the first is Fleming's hand rules the second is the Palm rule. This video discusses both.
Both are equally valid, however it is best to consistently use one or the other.

Charge behaviour in an Magnetic field

Interactive
Let's start by first examing this simulation ​ (By Tom Walsh) of a charged particle being shot into a magnetic field.
  1. Set the variables and fire a charge in the field
    What do you observe?
​​

As demonstrated in the simulation, a moving charged particle deflected by a magnetic field follows a distinct circular arc.

The Lorentz Force & Circular Motion

When a charge q moves with velocity v through an external magnetic field B, it experiences a magnetic force (FB) described by the magnetic component of the Lorentz Force Law:

FB = qvB sin(θ)

Where θ is the angle between the particle's velocity vector and the magnetic field vector. According to the Right-Hand Palm Rule (or Fleming's Left-Hand Rule), this magnetic force acts strictly perpendicular to both the direction of motion and the magnetic field lines.

Because FB is always perpendicular to velocity, it acts as a centripetal force (Fc = mv2⁄r). It changes the direction of the particle's motion without altering its speed or kinetic energy. Equating centripetal force to the magnetic force when moving perpendicularly (θ = 90°) allows us to derive the radius (r) of the path:

qvB = mv2⁄r  & implies;  r = mv⁄qB

Watch the video below as we elaborate further on these mathematical relationships and explore how varying mass, charge, velocity, and field strength influence particle trajectories.

 Check your understanding

Check Your Understanding: Charge Trajectories in Magnetic Fields

Question: An electron and a proton enter the same uniform magnetic field with equal velocities perpendicular to the field lines. How do the radii (r) and directions of their circular paths compare?

Interactive
Let's now revisit the interactive above. The instructions below allow you to consolidate and test your understanding.
  1. Set the variables to some value
  2. Fire a trace
  3. Change ONE variable, keeping all others constant and PREDICT what will happen
  4. Fire the trace to test your prediction.
    Can you explain the trace?
  5. Repeat for another variable
Sample Problem
We are now ready to try a sample problem
Below is a sample problem with a video that explain how to solve it. It is suggested you try the problem beforehand, as this actually aids understanding, even if you are unsure if you are correct.
Picture
More problems to try
  1. 1. An unknown particle having a mass of 2.2 x 10-27 kg and a charge of 3.3 x 10–19 C passes through a magnetic field of 5.4 x 10-1 T. The velocity of the particle is 6.4 x 103 m/s. What is the radius of its path? (7.9 x 105 m)
  2. 2. A particle with a mass of 3.8 x 10-27 kg and a charge of 6.2 x 10–19 C crosses a magnetic field that measures 2.7 x 10-2 T. The particle assumes a circular path with a radius of 1.5 x 10-1 m. At what speed is the particle moving? (660, 790 m/s)
  3. 3. A particle passing through a magnetic field has a mass of 6.3 x 10–27 kg and is moving at 3.9 x 104 m/s. The charge on the particle is 2.4 x 10-18 C and the radius of its circular path through the field is 4.4 x 10-2 m. What is the strength of the magnetic field? (0.00233 T)
  4. 4. A particle with a mass of 3.34 x 10-27 kg and a charge of 1.2 x 10-19 C passes through a magnetic field of 3.4 x 10-3 T. This causes the nucleus to assume a circular path with a radius of 0.065 m. What is its velocity? (4940.1 m/s)

How well do you know charge behaviour in fields?

Having now covered charge behaviour in both electric and magnetic fields, test your understanding of charges in fields.
Do the Quiz and try to get full marks

Then check your understanding if necessary with the video
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