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Temperature effects on resistancePermanent magnets and gaussmeter.Electromagnets - BigBite for ResearchForce on a wire in a magnetic field - DemoForce on a coil in a magnetic field - DemoCrossed E/B fields. Discovery of the electronLecture 9 starts here
Torques on current loops
Electric motors operate by connecting a coil in a magnetic field to a current supply,
which produces a torque on the coil causing it to rotate.
Above is a rectangular loop of wire of sides a and b carrying current i.
B is in the plane of the loop.
Equal and opposite forces
are exerted on the sides
No forces exerted on
Since net force is zero, we can evaluate
(torque) about any point. Evaluate it
about P (cm).
For N loops we mult by N
the plane is perpendicular to B
Magnetic dipole moment is in the
same direction as the normal.
Electric field bends particle upwards
Magnetic field bends it downwards
E=0, B=0 Observe spot on screen
2. Set E to some value and measure y the deflection
3. Now turn on B until spot returns to the original position
This ratio was first measured by Thompson
to be lighter than hydrogen by 1000
4 Solve for
Show demo of CRT
How do you calculate the magnetic field
magnetic field from a moving charge
or from a current flowing in a wire?
What do the flux lines look like?
Demo Sprinkle iron filings around a wire carrying current
10 magnetic field8 m/s
A point charge q = 1 mC (1x10-3C) moves in the x direction with v = 108 m/s. It misses a mosquito by 1 mm. What is the B field experienced by the mosquito?
Topic: A current produces a magnetic field magnetic fieldRecall the E field of a charge distribution
To find the field of a current distribution use:
This Law is found from experiment
i magnetic field
is a vector coming out of the paper The angle between dl and r is constant and equal to 90 degrees.
iFind B field at center of loop of wire lying in a plane with radius R and total current i flowing in it.
Magnitude of B field at center of loop. Direction is out of paper.
i magnetic fieldExample
Loop of wire of radius R = 5 cm and current i = 10 A. What is B at the center? Magnitude and direction
Direction is out of the page.
Total length of arc is S.
where S is the arc length S = R0
0 is in radians (not degrees)
Why is the contribution to the B field at P equal to zero from
the straight section of wire?
Suppose you had the following loop arc of wire?.Find magnetic field at center of arc length
What is the magnitude and direction of B at the origin?
Current enclosed by the path arc of wire?
Ampere’s Law is
Next topic: Ampere’s Law
Allows us to solve certain highly symmetric current problems for the magnetic field as Gauss’ Law did in electrostatics.
This dl is along the Amperian loop not
along the wire. dl is the same as ds below
i arc of wire?
i = 10 A
R = 10 cm
Example: Use Ampere’s Law to find B near a very long, straight wire. B is independent of position along the wire and only depends on the distance from the wire (symmetry).
Show Fe fillings around a straight wire with current,
current loop, and solenoid.
Suppose one of the currents is in the opposite direction? What direction is ?
Find the force due to the current element of the first wire and the magnetic field of the second wire. Integrate over the length of both wires. This will give the force between the two wires.Force between two current carrying wires
(Given by Ampere’s Law)
The force is directed towards the wire (wires are attracted).
IC = current enclosed by the circle whose radius is r
Example: Find field inside a solenoid. See next slide.
n is the number of turns per meter
d What direction is ?
IC is the total current enclosed by the path
n is the the number of loops of current per meter and h is the length of one side.
First evaluate the right side of the integral , it’s easy
Right side =
d What direction is ?
Evaluate left side of the integral :
n = the number of loops or turns per meter
a < r < b What direction is ?
N is the total
number of turns
Tokamak Toroid at Princeton
I = 73,000 Amps for 3 secs
B = 5.2 T
Magnetic field lines for a bar magnet
and a current loop are similar
In Figure 29-36, two circular arcs have radii a = 13.1 cm and b = 10.6 cm, subtend angle θ = 74.0°, carry current i = 0.388 A, and share the same center of curvature P. What is the magnitude and direction of the net magnetic field at P? (Take out of the page to be positive.)
A 180 turn solenoid having a length of 22 cm and a diameter of 10 cm carries a current of 0.39 A. Calculate the magnitude of the magnetic field B inside the solenoid.
A student makes a short electromagnet by winding 150 turns of wire around a wooden cylinder of diameter d = 7.0 cm. The coil is connected to a battery producing a current of 4.0 A in the wire.
(b) At what axial distance z d will the magnetic field of this dipole have the magnitude 5.0 µT (approximately one-tenth that of Earth's magnetic field)?