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### Magnetic force

• 1. Magnetic force Dr Ehab Hegazy Magnetic field Dr. Ehab Hegazy
• 2.
• 3. Earth’s Magnetic Field •The source of the Earth’s magnetic field is likely convection currents in the Earth’s core. •There is strong evidence that the magnitude of a planet’s magnetic field is related to its rate of rotation. •The direction of the Earth’s magnetic field reverses periodically.
• 4.
• 5. October 31, 2007 Electric Field & Magnetic Field  Electric forces acting at a distance through electric field.  Vector field, E.  Source: electric charge.  Positive charge (+) and negative charge (-).  Opposite charges attract, like charges repel.  Electric field lines visualizing the direction and magnitude of E.  Magnetic forces acting at a distance through Magnetic field.  Vector field, B  Source: moving electric charge (current or magnetic substance, such as permanent magnet).  North pole (N) and south pole (S)  Opposite poles attract, like poles repel.  Magnetic field lines visualizing the direction and magnitude of B.
• 6.
• 7.
• 8.
• 9.
• 10.
• 11. Direction: Right-Hand Alternative to Rule #1 The force on a positive charge extends outward from the palm. The advantage of this rule is that the force on the charge is in the direction you would push on something with your hand. The force on a negative charge is in the opposite direction.
• 12.
• 13.
• 14.
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• 16.
• 17.
• 18.
• 19.
• 20.
• 21.
• 22.
• 23.
• 24. Velocity Selector Used when all the particles need to move with the same velocity. A uniform electric field is perpendicular to a uniform magnetic field. When the force due to the electric field is equal but opposite to the force due to the magnetic field, the particle moves in a straight line. This occurs for velocities of value. v = E / B
• 25. Mass Spectrometer A mass spectrometer separates ions according to their mass-to-charge ratio. In one design, a beam of ions passes through a velocity selector and enters a second magnetic field. After entering the second magnetic field, the ions move in a semicircle of radius r before striking a detector at P. If the ions are positively charged, they deflect to the left. If the ions are negatively charged, they deflect to the right.
• 26. Example  A proton is released from rest at a point which is located next to the positive plate of a parallel plate capacitor.  The proton then accelerates toward the negative plate, leaving the plate through a small hole in the capacitor. The electric potential of the positive plate is 2100 V greater than the negative plate.  Once outside of the capacitor, the proton encounters a magnetic field of 0.10 T. The velocity is perpendicular to the magnetic field.  Find the speed of the proton when it leaves the capacitor, and the radius of the circular path on which the proton moves in the magnetic field.
• 27. Solution  The only force that acts on the proton while it is between the capacitor plates is the conservative electric force. Thus: ffoo qVmvqVmv  22 2 1 2 1
• 28. Solution cont.  If we note that the initial velocity is zero and that the charge of the proton is equal in magnitude to that of the electron we can write the following: )( 2 1 2 fof VVemv 
• 29. Solution cont.  Solving for the speed we get:      smv kg VC mVVe v f fo f /103.6 1067.1 2100106.12 /2 5 27 19        
• 30. Solution cont.  When the proton moves in the magnetic field, the radius of the circular path is:       mr TC smkg eB mv r f 2 19 527 106.6 10.01060.1 /103.61067.1       
• 31. Charged Particles Moving in Electric and Magnetic Fields In many applications, charged particles will move in the presence of both magnetic and electric fields. In that case, the total force is the sum of the forces due to the individual fields.  The total force is called the Lorentz force. In general: q q  F E v B r r rr
• 32. Velocity Selector, cont. Only those particles with the given speed will pass through the two fields undeflected. The magnetic force exerted on particles moving at a speed greater than this is stronger than the electric field and the particles will be deflected to the left. Those moving more slowly will be deflected to the right.
• 33. Example: If a proton moves in a circle of radius 21 cm perpendicular to a B field of 0.4 T, what is the speed of the proton and the frequency of motion? v r x x x x 1 m qB f 2  kg TC f 27 19 1067.12 4.0106.1       HzHzf 68 101.610 67.128.6 4.06.1     Hzf 6 101.6  2 m qBr v  kg mTC v 27 19 1067.1 21.04.0106.1      s m s m v 68 101.810 67.1 21.04.06.1    s m v 6 101.8 
• 34.
• 35.
• 36. An electron is accelerated through a potential difference of 1.0 kV and directed into a region between two parallel plates separated by 20 mm with a potential difference of 100 V between them. The electron is moving perpendicular to the electric field of the plates when it enters the region between the plates. What uniform magnetic field, applied perpendicular to both the electron path and the electric field, will allow the electron to travel in a straight line
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