Mass training of trainers General Physics 2 May 23-25, 2017 Magnetic Field, Magnetic Force, Magnetic flux, Motion of Moving Charge, DC-Motor Prof. MARLON FLORES SACEDON Physics Instructor Visayas State University Baybay City, Leyte

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magnetism Magnetism is a class of physical phenomena that are mediated by magnetic fields. Electric currents and the magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. Magnetic phenomena were first observed at least 2500 years ago in fragments of magnetized iron ore found near the ancient city of Magnesia (now Manisa, in western Turkey). These fragments were what are now called permanent magnets;

magnetism

magnetism Magnetic field about a conductor

Magnetic forces on Moving Charges Electric interaction can be represented in two steps: A distribution of electric charge creates an electric field 𝐸 in the surrounding space. The electric field exerts a force 𝐹 =𝑞 𝐸 on any other charge 𝑞 that is present in the field. Magnetic interaction can be describe in similar way: A moving charge or a current creates a magnetic field in the surrounding space. The magnetic field exerts a force 𝐹 on any other moving charge or current that is present in the field. 𝐵 + 𝑣

Magnetic forces on Moving Charges Electric interaction can be represented in two steps: A distribution of electric charge creates an electric field 𝐸 in the surrounding space. The electric field exerts a force 𝐹 =𝑞 𝐸 on any other charge 𝑞 that is present in the field. Magnetic interaction can be describe in similar way: A moving charge or a current creates a magnetic field in the surrounding space. The magnetic field exerts a force 𝐹 on any other moving charge or current that is present in the field. 𝐹=𝑞𝑣𝐵𝑠𝑖𝑛∅ + 𝑣 𝐹 =0 Where: 𝐹 = magnitude of magnetic force/Lorentz force (N) 𝑞 = particle’s charge (C) 𝐵 = magnitude of magnetic field (T) 𝑣 = speed of charge (m/s) ∅ = angle from 𝑣 to 𝐵 𝐵 𝐵 + 𝐹 𝑣 ∅ Note: Unit of 𝐵 Tesla = 𝑇 = N/A.m If ∅= 90 𝑜 𝐹=𝑞𝑣𝐵

MagnetIc Field Lines

MagnetIc Field Lines

MagnetIc Flux Magnetic flux is a scalar quantity. If 𝐵 is uniform over a plane surface with total area A, then 𝐵 ⊥ and 𝜙 are the same at all points on the surface,

Motion of moving particle in a magnetic field “Motion of a charged particle under the action of a magnetic field alone is always motion with constant speed.” Where: 𝐹 is magnetic force [N] 𝑣 is velocity of charge particle [m/s] 𝑚 is mass of charge particle [kg] 𝐹 is magnetic field 𝜔 is angular frequency [rad/s]] 𝑓 is frequency [Hz]

Motion of moving particle in a magnetic field

Velocity Selector

Velocity Selector Thomson’s e/m Experiment

Magnetic force on a Current-Carrying Conductor What makes an electric motor work? Within the motor are conductors that carry currents (that is, whose charges are in motion), as well as magnets that exert forces on the moving charges. Hence there is a magnetic force on each current-carrying conductor, and these forces make the motor turn. 𝐹=𝑞𝑣𝐵 Where: 𝐹 = Lorent force (N) 𝐼 = Current (A) 𝑙 = Length of conductor (m) 𝐵 = Magnetic field (T) 𝐹=𝐼𝑙𝐵 If ∅= 90 𝑜

Magnetic force on a Current-Carrying Conductor

Magnetic force on a Current-Carrying Conductor

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.”

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.” 𝑩 𝑩 𝑰 𝑭 ⊙ 𝑭 ⨂ FRONT VIEW 𝑭 90 𝑂 −∅ 𝑰 𝑏𝑠𝑖𝑛∅ 2 𝑏 ∅ 𝑭 ′ − 𝑭 𝑎 SIDE VIEW 𝐹 𝑛𝑒𝑡 = sum of all forces on the four sides of the loop 𝐹 𝑛𝑒𝑡 = 𝐹 + − 𝐹 + 𝐹 ′ +(− 𝐹 ′ ) =0 𝐹 =𝐼𝑎𝐵𝑠𝑖𝑛( 90 𝑜 −∅) 𝐹 ′=𝐼𝑏𝐵𝑠𝑖𝑛 90 𝑜

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.” 𝑩 𝑩 𝑰 𝑭 ⊙ 𝑭 ⨂ FRONT VIEW 𝝁 𝑭 =𝐼𝑎𝐵 90 𝑂 −∅ 𝑰 ∅ 𝑏𝑠𝑖𝑛∅ 2 𝑏 ∅ 𝝉 𝝁 ⨂ 𝑭 ′ − 𝑭 𝑎 SIDE VIEW Torque ( 𝜏 ) is force time lever arm 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 2 +(− 𝐹 ) − 𝑏𝑠𝑖𝑛∅ 2 Potential energy (𝑈) of magnetic dipole 𝜏 =𝐼𝐴𝐵𝑠𝑖𝑛∅ Note: Magnetic dipole moment ( 𝜇 ) is current times area of loop 𝑈=− 𝜇 ⋅ 𝐵 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 𝜏 =(𝐼𝑎𝐵)(𝑏𝑠𝑖𝑛∅) 𝜏=𝜇𝐵𝑠𝑖𝑛∅ 𝜏 =𝐼𝑎𝑏𝐵𝑠𝑖𝑛∅ 𝜏 = 𝜇 × 𝐵

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.” 𝑩 𝑩 𝑰 𝑭 ⊙ 𝑭 ⨂ FRONT VIEW 𝑭 𝑰 𝑏 − 𝑭 𝑭 𝝁 ⨂ − 𝑭 𝑎 SIDE VIEW Torque ( 𝜏 ) is force time lever arm 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 2 +(− 𝐹 ) − 𝑏𝑠𝑖𝑛∅ 2 Potential energy (𝑈) of magnetic dipole 𝜏 =𝐼𝐴𝐵𝑠𝑖𝑛∅ Note: Magnetic dipole moment ( 𝜇 ) is current times area of loop 𝑈=− 𝜇 ⋅ 𝐵 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 𝜏 =(𝐼𝑎𝐵)(𝑏𝑠𝑖𝑛∅) 𝜏 =𝜇𝐵𝑠𝑖𝑛∅ 𝜏 =𝐼𝑎𝑏𝐵𝑠𝑖𝑛∅ 𝜏 = 𝜇 × 𝐵

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.” 𝑩 𝑩 𝑰 𝑭 ⊙ 𝑭 ⨂ FRONT VIEW 𝝁 𝑭 𝑰 𝑏 𝝁 ⨂ − 𝑭 𝑎 SIDE VIEW Torque ( 𝜏 ) is force time lever arm 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 2 +(− 𝐹 ) − 𝑏𝑠𝑖𝑛∅ 2 Potential energy (𝑈) of magnetic dipole 𝜏 =𝐼𝐴𝐵𝑠𝑖𝑛∅ Note: Magnetic dipole moment ( 𝜇 ) is current times area of loop 𝑈=− 𝜇 ⋅ 𝐵 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 𝜏 =(𝐼𝑎𝐵)(𝑏𝑠𝑖𝑛∅) 𝜏 =𝜇𝐵𝑠𝑖𝑛∅ 𝜏 =𝐼𝑎𝑏𝐵𝑠𝑖𝑛∅ 𝜏 = 𝜇 × 𝐵

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.” 𝑩 𝑩 𝑰 𝑭 ⊙ 𝑭 ⨂ FRONT VIEW 𝑭 𝑰 𝑏 𝝁 ∅ 𝝁 ⨂ 𝑎 − 𝑭 SIDE VIEW Torque ( 𝜏 ) is force time lever arm 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 2 +(− 𝐹 ) − 𝑏𝑠𝑖𝑛∅ 2 Potential energy (𝑈) of magnetic dipole 𝜏 =𝐼𝐴𝐵𝑠𝑖𝑛∅ Note: Magnetic dipole moment ( 𝜇 ) is current times area of loop 𝑈=− 𝜇 ⋅ 𝐵 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 𝜏 =(𝐼𝑎𝐵)(𝑏𝑠𝑖𝑛∅) 𝜏 =𝜇𝐵𝑠𝑖𝑛∅ 𝜏 =𝐼𝑎𝑏𝐵𝑠𝑖𝑛∅ 𝜏 = 𝜇 × 𝐵

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.” 𝑩 𝑩 𝑰 𝑭 ⊙ 𝑭 ⨂ FRONT VIEW 𝑭 𝑰 𝑏 − 𝑭 𝑭 𝝁 ⨂ 𝑎 − 𝑭 SIDE VIEW Torque ( 𝜏 ) is force time lever arm 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 2 +(− 𝐹 ) − 𝑏𝑠𝑖𝑛∅ 2 Potential energy (𝑈) of magnetic dipole 𝜏 =𝐼𝐴𝐵𝑠𝑖𝑛∅ Note: Magnetic dipole moment ( 𝜇 ) is current times area of loop 𝑈=− 𝜇 ⋅ 𝐵 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 𝜏 =(𝐼𝑎𝐵)(𝑏𝑠𝑖𝑛∅) 𝜏 =𝜇𝐵𝑠𝑖𝑛∅ 𝜏 =𝐼𝑎𝑏𝐵𝑠𝑖𝑛∅ 𝜏 = 𝜇 × 𝐵

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.” 𝑩 𝑩 𝑰 𝑭 ⊙ 𝑭 ⨂ FRONT VIEW 𝑭 𝑰 𝝁 𝑏 −∅ 𝝁 ⨂ − 𝑭 𝑎 SIDE VIEW Torque ( 𝜏 ) is force time lever arm 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 2 +(− 𝐹 ) − 𝑏𝑠𝑖𝑛∅ 2 Potential energy (𝑈) of magnetic dipole 𝜏 =𝐼𝐴𝐵𝑠𝑖𝑛∅ Note: Magnetic dipole moment ( 𝜇 ) is current times area of loop 𝑈=− 𝜇 ⋅ 𝐵 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 𝜏 =(𝐼𝑎𝐵)(𝑏𝑠𝑖𝑛∅) 𝜏 =𝜇𝐵𝑠𝑖𝑛∅ 𝜏 =𝐼𝑎𝑏𝐵𝑠𝑖𝑛∅ 𝜏 = 𝜇 × 𝐵

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.” 𝑩 𝑩 𝑰 𝑭 ⊙ 𝑭 ⨂ FRONT VIEW 𝝁 𝑰 𝑏 − 𝑭 𝑭 𝝁 ⨂ 𝑎 SIDE VIEW Torque ( 𝜏 ) is force time lever arm 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 2 +(− 𝐹 ) − 𝑏𝑠𝑖𝑛∅ 2 Potential energy (𝑈) of magnetic dipole 𝜏 =𝐼𝐴𝐵𝑠𝑖𝑛∅ Note: Magnetic dipole moment ( 𝜇 ) is current times area of loop 𝑈=− 𝜇 ⋅ 𝐵 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 𝜏 =(𝐼𝑎𝐵)(𝑏𝑠𝑖𝑛∅) 𝜏 =𝜇𝐵𝑠𝑖𝑛∅ 𝜏 =𝐼𝑎𝑏𝐵𝑠𝑖𝑛∅ 𝜏 = 𝜇 × 𝐵

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.” 𝑩 𝑩 𝑰 𝑭 ⊙ 𝑭 ⨂ FRONT VIEW 𝑭 𝑰 𝝁 𝑏 −∅ 𝝁 ⨂ − 𝑭 𝑎 SIDE VIEW Torque ( 𝜏 ) is force time lever arm 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 2 +(− 𝐹 ) − 𝑏𝑠𝑖𝑛∅ 2 Potential energy (𝑈) of magnetic dipole 𝜏 =𝐼𝐴𝐵𝑠𝑖𝑛∅ Note: Magnetic dipole moment ( 𝜇 ) is current times area of loop 𝑈=− 𝜇 ⋅ 𝐵 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 𝜏 =(𝐼𝑎𝐵)(𝑏𝑠𝑖𝑛∅) 𝜏 =𝜇𝐵𝑠𝑖𝑛∅ 𝜏 =𝐼𝑎𝑏𝐵𝑠𝑖𝑛∅ 𝜏 = 𝜇 × 𝐵

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.” 𝑩 𝑩 𝑰 𝑭 ⊙ 𝑭 ⨂ FRONT VIEW 𝑭 𝑰 𝑏 𝝁 ∅ 𝝁 ⨂ 𝑎 − 𝑭 𝜏 =𝑁𝐼𝐴𝐵𝑠𝑖𝑛∅ SIDE VIEW Where: N is the numbers turns Torque ( 𝜏 ) is force time lever arm 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 2 +(− 𝐹 ) − 𝑏𝑠𝑖𝑛∅ 2 Potential energy (𝑈) of magnetic dipole 𝜏 =𝐼𝐴𝐵𝑠𝑖𝑛∅ Note: Magnetic dipole moment ( 𝜇 ) is current times area of loop 𝑈=− 𝜇 ⋅ 𝐵 𝜏 = 𝐹 𝑏𝑠𝑖𝑛∅ 𝜏 =(𝐼𝑎𝐵)(𝑏𝑠𝑖𝑛∅) 𝜏 =𝜇𝐵𝑠𝑖𝑛∅ 𝜏 =𝐼𝑎𝑏𝐵𝑠𝑖𝑛∅ 𝜏 = 𝜇 × 𝐵

force and torqUe on a cUrrent loop “The net force on a current loop in a uniform magnetic field is zero. However, the net torque is not in general equal to zero.” 𝑩 𝑩 𝑰 𝑭 ⊙ 𝑭 ⨂ FRONT VIEW 𝑭 𝑰 𝑏 𝝁 𝝉 ∅ 𝝁 ⨂ 𝑎 − 𝑭 SIDE VIEW 𝜇 =𝑁𝐼𝐴 SUMMARY 𝜏 = 𝜇 × 𝐵 𝑈=− 𝜇 ⋅ 𝐵

The Direct-Current Motor

10 Minutes DC Motor 1 meter Magnetic wire gauge 21 9 volts battery 9v battery wire connector Permanent magnet Cutter Styrofoam AA battery (used)

10 Minutes DC Motor 1 2 3 4 5 6

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