Chapter 29. Magnetic Field Due to Currents 29.1. What is Physics? 29.2. Calculating the Magnetic Field Due to a Current 29.3. Force Between Two Parallel.

Chapter 29. Magnetic Field Due to Currents

29.1. What is Physics?      29.2. Calculating the Magnetic Field Due to a Current      29.3. Force Between Two Parallel Currents      29.4. Ampere's Law      29.5. Solenoids and Toroids      29.6. A Current-Carrying Coil as a Magnetic Dipole

What is Physics?

A moving charged particle produces a magnetic field around itself

Magnetic Field Due to a Current

A length vector     that has length ds and whose direction is the direction of the current in ds.

The permeability constant, whose value is defined to be exactly

Magnetic Field Due to a Current in a Long Straight

Wire

02

sin

4

i dsdB

r

Magnetic field lines produced by a current in a long straight wire

Right-hand rule

Grasp the element in your right hand with your extended thumb pointing in the direction of the current. Your fingers will then naturally curl around in the direction of the magnetic field lines due to that element.

Magnetic Field Due to a Current in a Circular Arc of Wire

2

A Current-Carrying Coil as a Magnetic

Dipole

0

2c

iB

R

For a loop, ϕ=2π, at the center of the loop

02 2 3/2

( )2 ( )

B zR z

If

Sample Problem The wire in Fig. 29-8a carries a current i and consists of a circular arc of radius R and central angle      rad, and two straight sections whose extensions intersect the center C of the arc. What magnetic field     does the current produce at C?

Example  Finding the Net Magnetic Field

A long, straight wire carries a current of I1=8.0 A. As Figure 21.31a illustrates, a circular loop of wire lies immediately to the right of the straight wire. The loop has a radius of R=0.030 m and carries a current of I2=2.0 A. Assuming that the thickness of the wires is negligible, find the magnitude and direction of the net magnetic field at the center C of the loop.

Two Current-Carrying Wires Exert Magnetic Forces on One Another

• To find the force on a current-carrying wire due to a second current-carrying wire, first find the field due to the second wire at the site of the first wire. Then find the force on the first wire due to that field.

• Parallel currents attract each other, and antiparallel currents repel each other.

 Ampere's Law

• The loop on the integral sign means that is to be integrated around a closed loop, called an Amperian loop. The current ienc is the net current encircled by that closed loop.

• Curl your right hand around the Amperian loop, with the fingers pointing in the direction of integration. A current through the loop in the general direction of your outstretched thumb is assigned a plus sign, and a current generally in the opposite direction is assigned a minus sign.

Example An Infinitely Long, Straight, Current-Carrying Wire

Use Ampere’s law to obtain the magnetic field produced by the current in an infinitely long, straight wire.

Magnetic Field Inside a Long Straight Wire with uniformly distributed Current

A LOOP OF Current

• For a single loop, the magnetic field at the center is: B=μ0I/(2R)

• For a loop with N turns of wire,

Comparison a loop wire and a bar magnet

• loop wire

• bar magnet

Magnetic Field of a Solenoid

For a long ideal solenoid

where n is the number of turns per unit length of the solenoid

Magnetic Field of a Toroid

Example  

A solenoid is 0.50 m long, has three layers of windings of 750 turns each, and carries a current of 4.0 A. What is the magnetic field at the center of the solenoid?

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