1. Sources of Magnetic Fields
Physics 4
Sources of Magnetic Fields
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2. Sources of Magnetic Field
How can you create a magnetic field?
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3. Sources of Magnetic Field
How can you create a magnetic field?
Answer: move some charges (e.g. make current flow in a wire)
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

4. Sources of Magnetic Field
How can you create a magnetic field?
Answer: move some charges (e.g. make current flow in a wire)
Here is a formula for the magnetic field near a current element:
𝑑 𝐵 = 𝜇 0 4𝜋 𝐼𝑑 𝑙 × 𝑟 𝑟 2
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

5. Sources of Magnetic Field
How can you create a magnetic field?
Answer: move some charges (e.g. make current flow in a wire)
Here is a formula for the magnetic field near a current element:
𝑑 𝐵 = 𝜇 0 4𝜋 𝐼𝑑 𝑙 × 𝑟 𝑟 2
To find the total B-field due to the current in a circuit we will integrate this expression along the entire circuit. Several examples in your book…
𝐵 = 𝜇 0 4𝜋 𝐼𝑑 𝑙 × 𝑟 𝑟 2
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6. Magnetic Field Near a Long Straight Wire
This formula gives the magnitude of the magnetic field near a wire. The B-field takes the shape of concentric rings centered on the wire. We get a new right-hand-rule.
To get the formula, integrate along the length of the wire using the setup pictured below. Details are in the book, but you should try it on your own for practice.
x = distance from wire
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7. 2 current-carrying wires will put magnetic forces on each other.
Wire #1 and #2 below both have current flowing to the right.
Find the direction of the magnetic force on each wire.
Wire #1 I1
Wire #2 I2
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8. 2 current-carrying wires will put magnetic forces on each other.
Wire #1 and #2 below both have current flowing to the right.
Find the direction of the magnetic force on each wire.
Wire #1 I1
Wire #2 I2
The magnetic field created by wire #1 is shown. The field points into the page in the vicinity of wire #2, creating magnetic force upward on wire #2.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

9. 2 current-carrying wires will put magnetic forces on each other.
Wire #1 and #2 below both have current flowing to the right.
Find the direction of the magnetic force on each wire.
Wire #1 I1
Wire #2 I2
Now we see the field created by wire #2. The field points out of the page in the vicinity of wire #1, creating magnetic force downward on wire #1.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

10. 2 current-carrying wires will put magnetic forces on each other.
Wire #1 and #2 below both have current flowing to the right.
Find the direction of the magnetic force on each wire.
Wire #1 I1
Wire #2 I2
Basic result:
Parallel curents - wires will attract each other
Anti-parallel currents - wires will repel.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

11. 2 current-carrying wires will put magnetic forces on each other.
Wire #1 and #2 below both have current flowing to the right.
Find the direction of the magnetic force on each wire.
Wire #1 I1
Wire #2 I2
Now find a formula for the magnitude of the force.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

12. 2 current-carrying wires will put magnetic forces on each other.
Wire #1 and #2 below both have current flowing to the right.
Find the direction of the magnetic force on each wire.
Wire #1 I1
Wire #2 I2
Now find a formula for the magnitude of the force per unit length.
Combine the formulas for force on a wire with the field created by a current:
Note that this force is the same for both wires – the two forces form an action/reaction pair, as you would expect from Newton’s 3rd Law
𝐹 𝑜𝑛 2 /𝑙= 𝐼 2 𝜇 0 𝐼 1 2𝜋𝑥 sin 90° = 𝜇 0 𝐼 1 𝐼 2 2𝜋𝑥
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13. Bar Magnets Prepared by Vince Zaccone
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14. Circular Current Loop 𝐵 𝑥 = 𝜇 0 𝐼 𝑎 2 2 𝑥 2 + 𝑎 2 3 2
Here is the formula for the magnetic field on the axis of a circular loop of current (derived in book):
𝐵 𝑥 = 𝜇 0 𝐼 𝑎 𝑥 2 + 𝑎
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15. Circular Current Loop 𝐵 𝑥 = 𝜇 0 𝐼 𝑎 2 2 𝑥 2 + 𝑎 2 3 2
Here is the formula for the magnetic field on the axis of a circular loop of current (derived in book):
𝐵 𝑥 = 𝜇 0 𝐼 𝑎 𝑥 2 + 𝑎
We get a new right-hand-rule for determining the direction of the B-field of a loop.
This is really just a shortcut for the rule we learned for the straight wire, but it is useful.
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16. Magnetic Field in a Solenoid (aka coil)
Solenoid (Coil)
A solenoid is just a tightly-wrapped coil of several loops of wire.
Magnetic Field in a Solenoid (aka coil)
Notice the direction of the field – it looks very much like a bar magnet. The B-field lines go in through the south pole and come out through the north pole. Inside the coil the field is nearly uniform and points along the axis.
The strength of the field can be increased by inserting an iron core.
n is the number of loops per meter
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For Campus Learning Assistance Services at UCSB

17. Summary of Magnetic Field Formulas
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