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W06D2 Magnetic Forces and Sources of Magnetic Fields

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W06D2 Magnetic Force on Current Carrying Wire, Sources of Magnetic Fields: Biot-Savart Law

Reading Course Notes: Sections 8.3, 9.1-9.2

Review Week 6 Tuesday from 9-11 pm in 26-152

PS 6 due Week 6 Tuesday at 9 pm in boxes outside 32-082 or 26-152

W06D3 PS05: Calculating Magnetic Fields and Magnetic Force Reading Course Notes: Sections 8.9, 8.10, 9.10.1, 9.11.1-.3, 9.11.7-.8

Exam 2 Thursday March 21 7:30 - 9:30 pm

Conflict Exam 2 March 22 9-11 am or 10-12 noon

Announcements

Magnetic Force on Current Carrying Wire

Sources of Magnetic Fields

Biot-Savart Law

Current is moving charges, and we know that moving charges feel a force in a magnetic field

If the wire is a uniform magnetic field then

If the wire is also straight then

http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%208&show=0

Demonstration:Series or Parallel Current Carrying Wires G9

http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%209&show=0

You tube video of experiment showing parallel wires attracting

http://youtu.be/rU7QOukFjTo

or repelling:

http://youtu.be/bnbKdbXofEI

A conducting rod of uniform mass per length l is suspended by two flexible wires in a uniform magnetic field of magnitude B which points out of the page and a uniform gravitational field of magnitude g pointing down. If the tension in the wires is zero, what is the magnitude and direction of the current in the rod?

Sources of Magnetic Fields

What Creates Magnetic Fields: Moving Charges

http://youtu.be/JmqX1GrMYnU

An electric charge produces an electric field:

: unit vector directed from the charged object

to the field point P

Moving charge with velocity v produces magnetic field:

P

unit vector directed from charged object to P

permeability of free space

Currents are Sources of Magnetic Field

Demonstration:Field Generated by Wire G12

http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%2012&show=0

Continuous Moving Charge Distributions:Currents & Biot-Savart

Current element of length ds pointing in direction of current I produces a magnetic field:

http://web.mit.edu/viz/EM/visualizations/magnetostatics/MagneticFieldConfigurations/CurrentElement3d/CurrentElement.htm

The magnetic field at P points towards the

- +x direction
- +y direction
- +z direction
- -x direction
- -y direction
- -z direction
- Field is zero

Answer: 6. is in the negative z direction (into page)

The vertical line segment contributes nothing to the field at P (it is parallel to the displacement). The horizontal segment makes a field pointing into the page by the right-hand rule # 2 (right thumb in direction of current, fingers curl into page at P.

The magnetic field at P is equal to the field of:

- a semicircle
- a semicircle plus the field of a long straight wire
- a semicircle minus the field of a long straight wire
- none of the above

Answer: 2. Semicircle + infinite wire

All of the wire makes into the page. The two straight parts, if put together, would make an infinite wire. The semicircle is added to this to get the magnetic field

Repeat Demonstration:Parallel & Anti-Parallel Currents G9

http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%209&show=0

Consider two parallel current carrying wires. With the currents running in the opposite direction, the wires are

- attracted (opposites attract?)
- repelled (opposites repel?)
- pushed another direction
- not pushed – no net force
- I don’t know

Answer: 1. The wires are repelled

I1 creates a magnetic field into the

page at wire 2. That makes a force

on wire 2 to the right.

I2 creates a magnetic field into the

page at wire 1. That makes a force

on wire 1 to the left.

Whether they attract or repel can be seen in the shape of the created B field

http://youtu.be/5nKQjKgS9z0

http://youtu.be/nQX-BM3GCv4

You tube videos of field line animations showing why showing parallel wires attract: or repel:

- parallel currents that attract
- parallel currents that repel
- opposite currents that attract
- opposite currents that repel

The above coils have

Look at the field lines at the edge between the coils. They are jammed in, want to push out. Also, must be in opposite directions

Answer: 4. Opposite currents that repel

http://web.mit.edu/viz/EM/visualizations/magnetostatics/ForceOnCurrents/MagneticForceRepel/MagneticForceRepel.htm

Consider a coil with radius R and current I

Find the magnetic field B at the center (P)

Consider a coil with radius R and current I

- 1) Think about it:
- Legs contribute nothing

- I parallel to r
- Ring makes field into page

- 2) Choose a ds
- 3) Pick your coordinates
- 4) Write Biot-Savart

Animation: Magnetic Field Generated by a Current Loop

http://web.mit.edu/viz/EM/visualizations/magnetostatics/calculatingMagneticFields/RingMagInt/RingMagIntegration.htm

In the circular part of the coil…

Biot-Savart:

Consider a coil with radius R and current I

direction into page

Consider a coil with radius R and carrying a current I

WARNING:

This is much harder than the previous problem. Why??

What is B at point P?