Magnetic Force

F = qvB sin q Strength of Magnetic Force A charged particle moving in a magnetic field experiences a force that is perpendicular to BOTH the particle’s velocity and to the magnetic field itself. Lorentz Force Law: The magnitude of the magnetic force on a moving, charged particle is F = qvB sin q . Lorentz - Dutch physicist q = charge [C] V = velocity [m/s] B = magnetic field [T] q = the angle between the charge’s velocity and the magnetic field The unit of magnetic field, B, is Tesla (T) in honor of Nikola Tesla 1 T = 1 N·s/(C·m)

F = qvB sin q Sin 0, 180 = 0 If a charge has velocity in the same (or opposite) direction of the magnetic field, it experiences no force! Sin 90 = 1 A charge that has velocity perpendicular to the magnetic field experiences the greatest force!

Question? The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field. Which particle experiences the greatest magnetic force? 1 2 3 Same B 3 F = q v B sin q 2 1

The direction of the magnetic force is given by the Right-Hand Rule #1 positive charge ► Point fingers in v (or current I) direction v B q ► Curl fingers as if rotating vector v (current I) into B. ► Thumb is in the direction of the force. F negative charge ● For negative charge force is in the opposite direction . charge q moving with velocity v in the mag. field B F is perpendicular to the plane of v and B

Right Hand Rule Practice Convention for magnetic field direction: x x x x x x x INTO Page ••••••••••••• OUT of Page Right Hand Rule Practice A proton enters a magnetic field, as shown. Which way will the electron turn? Up Down Out of page Into page

Right Hand Rule Practice Convention for magnetic field direction: x x x x x x x INTO Page ••••••••••••• OUT of Page Right Hand Rule Practice A proton enters a magnetic field, as shown. Which way will the electron turn? Up Down Out of page Into page Put your fingers in the direction of the velocity and curl out of the page … your thumb points up

Right Hand Rule Practice Convention for magnetic field direction: x x x x x x x INTO Page ••••••••••••• OUT of Page Right Hand Rule Practice An electron enters a magnetic field, as shown. Which way will the electron turn? Up Down Out of page Into page

Right Hand Rule Practice Convention for magnetic field direction: x x x x x x x INTO Page ••••••••••••• OUT of Page Right Hand Rule Practice An electron enters a magnetic field, as shown. Which way will the electron turn? Up Down Out of page Into page Remember to flip the direction of the force for negative charges

Right Hand Rule Practice Convention for magnetic field direction: x x x x x x x INTO Page ••••••••••••• OUT of Page Right Hand Rule Practice In which direction will wire segment B be pushed? Up Down Out of page Into page No force exists

Right Hand Rule Practice Convention for magnetic field direction: x x x x x x x INTO Page ••••••••••••• OUT of Page Right Hand Rule Practice In which direction will wire segment B be pushed? Up Down Out of page Into page No force exists

Right Hand Rule Practice Convention for magnetic field direction: x x x x x x x INTO Page ••••••••••••• OUT of Page Right Hand Rule Practice In which direction will wire segment C be pushed? Up Down Out of page Into page No force exists

Right Hand Rule Practice Convention for magnetic field direction: x x x x x x x INTO Page ••••••••••••• OUT of Page Right Hand Rule Practice In which direction will wire segment C be pushed? Up Down Out of page Into page No force exists V and B are in the same direction; no force exists.

Magnetic Field & Magnetic Force Problems We do: What is the minimum magnetic field necessary to exert a 5.4 X 10-15 N force on an electron moving at 2.1 X 107 m/s?

Magnetic Field & Magnetic Force Problems We do: What is the minimum magnetic field necessary to exert a 5.4 X 10-15 N force on an electron moving at 2.1 X 107 m/s? B = F / qvsinθ B will be at a minimum when sin θ = 1 B = F / qv = 5.4X10-15N / (1.6 X 10-19 C X 2.1 X 107 m/s) B = 1.61 X 10-3 T

Magnetic Field & Magnetic Force Problems You do: What is the magnetic field necessary to exert a 5.4 X 10-15 N force on an electron moving at 2.1 X 107 m/s if the magnetic field is at 45 degrees from the electron’s velocity?

Magnetic Field & Magnetic Force Problems You do: What is the magnetic field necessary to exert a 5.4 X 10-15 N force on an electron moving at 2.1 X 107 m/s if the magnetic field is at 45 degrees from the electron’s velocity? B = F / qvsinθ = 5.4X10-15N / (1.6 X 10-19 C X 2.1 X 107 m/s X sin 45) B = 2.3 X 10-3 T.

Magnetic Fields can be used to generate electricity! If a conductor is moved through a magnetic field, the charges are pushed by the magnetic force. This leads to an accumulation of charge -- or potential difference -- on one side of the conductor. This process is called electromagnetic induction. If connected to a circuit, this induced potential difference (emf!) will cause a current to flow. Electric induction underlies MANY devices including electric generators electric motors transformers Etc, etc, etc. Movement or flux is key … a stationary conductor can be placed in a changing magnetic field or a conductor can be moved through magnetic field

V = lvB Magnetic Fields can be used to generate electricity! In this class, we will just have to solve for one induction scenario: A conductor moved perpendicularly through a stationary magnetic field In this case, Where V = induced potential difference (emf) l = length of the conductor v = velocity of the conductor B = magnetic field strength V = lvB Movement or flux is key … a stationary conductor can be placed in a changing magnetic field or a conductor can be moved through magnetic field

Magnetic Fields can be used to generate electricity! Example: A potential difference of 9 volts is induced across a straight wire of 0.5 m long as it is moved at constant speed of 4 m/s perpendicularly through a magnetic field. What is the strength of the magnetic field? V = lvB B = 𝑉 𝑙𝑣 B = 9 𝑉 0.5 𝑚 4 𝑚/𝑠 = 4.5 T Movement or flux is key … a stationary conductor can be placed in a changing magnetic field or a conductor can be moved through magnetic field

Electricity can be used to generate magnetic fields! Example: Solenoids. A solenoid is a coil of current-carrying wire. As the current goes through the coil it creates a strong, uniform magnetic field through the center of the coil. More current and more coils = stronger magnetic field We already know that electricity can be used to make magnetic fields (e.g. electromagnets). Most electromagnets are solenoids. ▪ If we place an iron core inside the solenoid we have an electromagnet. ▪The ferrous core enhances the strength of the B-field ▪ Used to create a strong, uniform magnetic field

RHR for Solenoids! Grasp the solenoid with your right hand in such a way that your fingers curl in the direction of the current. Your extended thumb points in the direction of north pole. PRACTICE: In the solenoid shown label the north and south poles. I © 2014 By Timothy K. Lund I PRACTICE: The north and south poles are labeled in the solenoid. Sketch in the current, both entering and leaving the solenoid.