# Section 30 Ampere's Law.

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Ideas to Know. Attractive Forces between wiresAmpere\'s lawSolenoidToroid. Attractive Forces Between Wires. Section 30.2Similar to strengths between two charged particlesGive 2 parallel wires 1
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﻿Section 30 Ampere\'s Law PHYS 2326-19

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Concepts to Know Magnetic Forces between wires Ampere\'s law Solenoid Toroid

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Magnetic Forces Between Wires Chapter 30.2 Similar to strengths between two charged particles Give 2 parallel wires 1 & 2 isolated by separation a with streams I1 & I2 What are the powers between them? B2 1 I1 F1 2 I2 a

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Magnetic Force Between 2 Wires Wire 2 produces a field B 2 For a long straight wire B 2 is from eqn 30.5 Force F 1 on wire 1 originates from eqn 29.10 Using sizes eqn 30.12 Using right hand rules for bearings B 2 is out of plane and F 1 is down towards wire 2

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Ampere\'s Law The line vital of B ·d s (B speck ds) is equivalent to μ o I (the penetrability of free space times the present I)

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The Toroid A ring or torus wrapped with a wire Create amperian circle – dashed line by symmetry (accept wire uniform the distance around) – the field is steady B and digression to it so B ·d s = B ds Wire goes through N times (4 appeared)

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The Toroid Since there are N turns, all out current through the circle is NI Apply Ampere\'s law

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. . . . . . . x The Solenoid Ideal solenoid is when length >> range B is uniform and parallel inside perfect solenoid Consider circle 2 a rectangle w*l in region Side 3 is far away so B = 0, side 2&4 B is opposite with the sides Side 1 is parallel and in a uniform field B so that the size is B l B circle 2 3 l 1 4 w circle 1

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Example 1 Given a rectangular circle of 10cm x 20cm (a by b) with counter clockwise current I=2A what is the size and course of attractive field at the middle point P B heading right hand preclude = of page B = Bab+Bbc+Bcd+Bda = 2Bab + 2Bbc a d I P b c

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Example 1 From eqn 30.4 for the field delivered by a long wire. The book demonstrates sines which is inverse/neighboring B = 8.78E-6 T

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Example 2 Long straight vertical wire conveys 10A A rectangular loop of wire situated close it conveys 5 An, a = 0.10m, b=0.30m, c=0.50m. Power on circle? Power on top = - Force on base b c I 2 I 1 a x

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Example 2

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Example 3 Use Ampere\'s Law to decide attractive field Choose a circle revolved around the wire so B is digression at each point and uniform in separation from the wire B d l r I

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Example 3 Dot item B · l = Bd l Same greatness at every point (symmetry) B is steady so

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Example 4 Inside and outside a Toroid Find the attractive field an) inside and b) outside a firmly twisted toroid of N turns

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