Fields Magnetic and Forces
AP Physics B
Aim: How do we calculate magnetic forces?
LO's Calculate the magnitude and direction of the force in terms of q, v, and, B, Describe the paths of charged particles moving in uniform magnetic fields.
Facts about Magnetism
Magnets have 2 poles (north and south) Like poles repel Unlike poles attract Magnets create a MAGNETIC FIELD around them
Magnetic Field
A bar magnet has a magnetic field around it. This field is 3D in nature and often represented by lines LEAVING north and ENTERING south To define a magnetic field you need to understand the MAGNITUDE and DIRECTION We sometimes call the magnetic field a B-Field as the letter "B" is the SYMBOL for a magnetic field with the TESLA (T) as the unit.
Magnetic Force on a moving charge
S N vo B S N
If a MOVING CHARGE moves into a magnetic field it will experience a MAGNETIC FORCE. This deflection is 3D in nature.
FB = qv B FB = qvB sin
The conditions for the force are: Must have a magnetic field present Charge must be moving Charge must be positive or negative Charge must be moving PERPENDICULAR to the field.
Magnetic fields will NOT perform work on a charge!! WHY????
Example
A proton moves with a speed of 1.0x105 m/s through the Earth's magnetic field, which has a value of 55T at a particular location. When the proton moves eastward, the magnetic force is a maximum, and when it moves northward, no magnetic force acts upon it. What is the magnitude and direction of the magnetic force acting on the proton?
FB = qvB, = 90, sin 90 = 1 FB = (1.6 x10 FB =
8.8x10-19 N
-19
)(1.0 x10 )(55 x10 )
5
-6
The direction cannot be determined precisely by the given information. Since no force acts on the proton when it moves northward (meaning the angle is equal to ZERO), we can infer that the magnetic field must either go northward or southward.
Direction of the magnetic force? Right Hand Rule To determine the DIRECTION of the
force on a POSITIVE charge we use a special technique that helps us understand the 3D/perpendicular nature of magnetic fields.
Basically you hold your right hand flat with your thumb perpendicular to the rest of your fingers
The Fingers = Direction B-Field The Thumb = Direction of velocity The Palm = Direction of the Force
For NEGATIVE charges use left hand!
Determine the direction of the unknown variable for a proton moving in the field using the coordinate axis given
+y +z +x
Example
B = -x v = +y F = +z
B =+Z v = +x F = -y
B = -z v = +y F = -x
Example
+y +z +x
Determine the direction of the unknown variable for an electron using the coordinate axis given.
B = +x v = +y F = +z
F B
B = -z v=-x F = +y
B = +z v = +x F = +y
Aim: How do we predict the path of a charged particle in a magnetic field?
LO's Derive and apply the formula for the radius of the circular path of a charge that moves perpendicular to a uniform magnetic field. Describe under what conditions particles will move with constant velocity through crossed electric and magnetic fields.
Magnetic Force and Circular Motion
v B X X X X X- X X X X XXXXXXXXX FB FB FB FB
XXXXXXXXX XXXXXXXXX -
-
Suppose we have an electron traveling at a velocity , v, entering a magnetic field, B, directed into the page. What happens after the initial force acts on the charge?
Derivation of Circular Path of Charge in Magnetic Field
Magnetic Force and Circular Motion
The magnetic force is equal to the centripetal force and thus can be used to solve for the circular path. Or, if the radius is known, could be used to solve for the MASS of the ion. This could be used to determine the material of the object.
There are many "other" types of forces that can be set equal to the magnetic force.
Example
A singly charged positive ion has a mass of 2.5 x 10-26 kg. After being accelerated through a potential difference of 250 V, the ion enters a magnetic field of 0.5 T, in a perpendicular direction to the field. Calculate the radius of the path of the ion in the field.
q = 1.6 x10 -19 C m = 2.5 x10 V = 250V B = 0.5T r =?
W K V = = = q q 1 2mv 2 q
- 26
kg
FB = Fc
mv 2 qvB = r
r=
mv qB
We need to solve for the velocity!
(2.5 x10 -26 )(56,568) r= = -19 (1.6 x10 )(0.5)
0.0177 m
2Vq 2(250)(1.6 x10 -19 ) v= = =56,568 m/s - 26 m 2.5 x10
Mass Spectrometers
Mass spectrometry is an analytical technique that identifies the chemical composition of a compound or sample based on the mass-to-charge ratio of charged particles. A sample undergoes chemical fragmentation, thereby forming charged particles (ions). The ratio of charge to mass of the particles is calculated by passing them through ELECTRIC and MAGNETIC fields in a mass spectrometer.
M.S. Area 1 The Velocity Selector
FB = FE
qvB = qE
E E = vB v = B
When you inject the sample you want it to go STRAIGHT through the plates. Since you have an electric field you also need a magnetic field to apply a force in such a way as to CANCEL out the electric force caused by the electric field.
M.S. Area 2 Detector Region
After leaving region 1 in a straight line, it enters region 2, which ONLY has a magnetic field. This field causes the ion to move in a circle separating the ions by mass. This is also where the charge to mass ratio can then by calculated. From that point, analyzing the data can lead to identifying unknown samples.
FB = Fc q v = m rB
mv qvB = r
2
Charges moving in a wire
Up to this point we have focused our attention on PARTICLES or CHARGES only. The charges could be moving together in a wire. Thus, if the wire had a CURRENT (moving charges), it too will experience a force when placed in a magnetic field.
You simply used the RIGHT HAND ONLY and the thumb will represent the direction of the CURRENT instead of the velocity.
Charges moving in a wire
t FB = qvB sin t q FB = ( )(vt ) B sin t FB = ILB sin
At this point it is VERY important that you understand that the MAGNETIC FIELD is being produced by some EXTERNAL AGENT
Example
A 36-m length wire carries a current of 22A running from right to left. Calculate the magnitude and direction of the magnetic force acting on the wire if it is placed in a magnetic field with a magnitude of 0.50 x10-4 T and directed up the page.
FB = ILB sin
+y +x
+z FB = (22)(36)(0.50 x10 - 4 ) sin 90 B = +y I = -x FB = 0.0396 N F = -z, into the page
WHY does the wire move?
The real question is WHY does the wire move? It is easy to say the EXTERNAL field moved it. But how can an external magnetic field FORCE the wire to move in a certain direction?
THE WIRE ITSELF MUST BE MAGNETIC!!! In other words the wire has its own INTERNAL MAGNETIC FIELD that is attracted or repulsed by the EXTERNAL FIELD.
As it turns out, the wire's OWN internal magnetic field makes concentric circles round the wire.
A current carrying wire's INTERNAL magnetic field
To figure out the DIRECTION of this INTERNAL field you use the right hand rule. You point your thumb in the direction of the current then CURL your fingers. Your fingers will point in the direction of the magnetic field
The MAGNITUDE of the internal field
The magnetic field, B, is directly proportional to the current, I, and inversely proportional to the circumference.
B I B
B
1 2r
I 2r o = vacuum permeability constant Tm o = 4 x10 (1.26 x10 ) A o I Binternal = 2r
-7 -6
A long, straight wires carries a current of 5.00 A. At one instant, a proton, 4 mm from the wire travels at 1500 m/s parallel to the wire and in the same direction as the current. Find the magnitude and direction of the magnetic force acting on the proton due to the field caused by the current carrying wire.
v X X X X X X X X X 4mm + X X X X X X X X X
Example
o I FB = qvBEX BIN = 2r (1.26 x10 -6 )(5) BIN = = 2.51 x 10- 4 T 2(3.14)(0.004)
5A
B = +z v = +y F = -x
FB = (1.6 x10 -19 )(1500)( Bwire ) =
6.02 x 10- 20 N