Lesson Notes By Weeks and Term v4 - SHS 2
ELECTROMAGNETISM
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ELECTROMAGNETISM
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Subject: Physics
Class: SHS 2
Term: 2nd Term
Week: 13
Grade code: 2.3.2.LI.2
Strand code: 3
Sub-strand code: 2
Content standard code: 2.3.2.CS.3
Indicator code: 2.3.2.LI.2
Theme: ELECTRIC FIELD, MAGNETIC FIELD AND ELECTRONICS
Subtheme: ELECTROMAGNETISM
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Welcome, students. Today, we are delving into a fascinating and powerful area of Physics called Electromagnetism. We have already learned about electric fields and magnetic fields separately. Now, we will explore what happens when a tiny charged particle, like an electron or a proton, moves through a space where *both* fields exist at the same time. This combined force is fundamental to how many technologies work, from the old box television sets (CRT TVs) some of us still have at home, to advanced medical equipment like MRI scanners in major hospitals like Korle-Bu, and even in scientific research at KNUST and the University of Ghana.
This topic builds on our previous knowledge. Let's review the two forces that make up the total force we will be studying. Part A: Review of Individual Forces Force on a Charged Particle in an Electric Field (Fₑ) Concept: When a particle with charge `q` is placed in an electric field `E`, it experiences a force. Formula: `Fₑ = qE` Explanation: `Fₑ` is the electric force in Newtons (N). `q` is the magnitude of the charge in Coulombs (C). `E` is the electric field strength in Newtons per Coulomb (N/C). Direction: For a positive charge (+q), the force `Fₑ` is in the same direction as the electric field `E`. For a negative charge (-q), the force `Fₑ` is in the opposite direction to the electric field `E`. This force acts on the charge whether it is stationary or moving. Force on a Charged Particle in a Magnetic Field (Fₘ) Concept: A magnetic field `B` exerts a force on a charged particle `q` *only if the particle is moving* with velocity `v`. Formula: `Fₘ = qvB sin(θ)` Explanation: `Fₘ` is the magnetic force in Newtons (N). `q` is the magnitude of the charge in Coulombs (C). `v` is the speed of the particle in metres per second (m/s). `B` is the magnetic field strength in Tesla (T). `θ` is the angle between the velocity vector `v` and the magnetic field vector `B`. Key Points: The force is maximum when the particle moves perpendicular to the field (`θ = 90°`, because `sin(90°) = 1`). The force is zero if the particle moves parallel or anti-parallel to the field (`θ = 0°` or `θ = 180°`, because `sin(0°) = sin(180°) = 0`). The force is zero if the particle is stationary (`v = 0`). Direction: The Right-Hand Slap Rule This rule helps us find the direction of the magnetic force on a positive charge. Point your four fingers in the direction of the Magnetic Field (B). Point your thumb in the direction of the Velocity (v) of the positive charge. The direction your palm would push is the direction of the Force (Fₘ). Important: If the charge is negative (like an electron), use the Right-Hand Slap Rule as normal, and then the actual force is in the exact opposite direction (i.e., out of the back of your hand). Part B: The Lorentz Force - Combining the Forces Definition: When a charged particle moves through a region with both an electric field `E` and a magnetic field `B`, the total force it experiences is called the Lorentz Force. It is the vector sum of the electric force and the magnetic force. Formula: `F_Total = Fₑ + Fₘ` `F_Total = qE + qvB sin(θ)` Explanation: Since `Fₑ` and `Fₘ` are vectors, we must consider their directions when adding them. The directions are often not the same, which leads to interesting effects. Part C: Crossed Fields and the Velocity Selector Definition: A "crossed field" is a special, very useful arrangement where the electric field `E` and the magnetic field `B` are perpendicular to each other. Application - The Velocity Selector: Imagine we want to select particles that are moving at a very specific speed from a beam containing particles with a range of speeds. We can use a crossed field to do this. Setup: An electric field `E` points downwards. A magnetic field `B` points into the page (represented by a circle with an 'X'). A beam of positive charges `+q` enters from the left with velocity `v`. Analysis of Forces: Electric Force (Fₑ): The charge is positive, and the E-field is down. So, `Fₑ` is downwards. Its magnitude is `Fₑ = qE`. Magnetic Force (Fₘ): Using the Right-Hand Slap Rule: Fingers point into the page (direction of B). Thumb points to the right (direction of v). Your palm pushes upwards. So, `Fₘ` is upwards. Since `v` and `B` are perpendicular (`θ = 90°`), its magnitude is `Fₘ = qvB`. The Condition for No Deflection: A particle will pass through in a straight line *only if the upward force exactly balances the downward force*. `Upward Force = Downward Force` `Fₘ = Fₑ` `qvB = qE`
We can cancel `q` from both sides: `vB = E`
Solving for the velocity `v`: `v = E / B` Conclusion: Only particles with this exact speed `v = E/B` will pass through undeflected. Faster particles (`v > E/B`): The magnetic force `Fₘ` will be stronger than the electric force `Fₑ`, so they will be deflected upwards. Slower particles (`v < E/B`): The electric force `Fₑ` will be stronger than the magnetic force `Fₘ`, so they will be deflected downwards. This device acts as a "velocity selector," allowing only particles of a desired speed to pass through a small exit slit.