PHYS1322-CH21Lec1 - Lecture 2 Lecture 2 Law of Electrical...

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Lecture 2 Lecture 2 Page 1 Lecture 2 Lecture 2 Page 2 Law of Electrical Force Charles-Augustin Coulomb 1785 " The force between two small charged spheres is proportional to the product of the charges and inversely proportional to the square of the distance between the centers of the spheres" 1 2 2 q q F r q 2 q 1 r Lecture 2 Page 3 MKS Units: r in meters q in Coulombs in Newtons is a unit vector pointing from 1 to 2 ε 0 is a constant of nature called “ permitivity of free space” q 2 q 1 12 r K Coulomb's Law The force on q 2 due to q 1 1 2 12 12 2 0 12 1 ˆ 4 q q F r r πε = G 1 4 πε = 9 · 10 9 Nm 2 /C 2 0 We often call this group of constants “ k ” as in: 1 2 12 12 2 12 ˆ q q F k r r = G F G 12 ˆ r Lecture 2 Page 4 q 2 q 1 12 r K Coulomb's Law This force has same form as the gravitational force with charge taking the place of mass The strength of the force between two objects is determined by the charge of the two objects, and the square of the separation between them. The direction of the force can be in the positive or negative direction depending on the signs of the charges Same sign charges – repulsion Opposite sign charges - attraction The force on q 2 due to q 1 12 2 12 2 1 0 12 ˆ 4 1 r r q q F πε = G Lecture 2 Page 5 Coulomb Law Qualitative q 2 r q 1 What happens to F if q 1 increases? F (magnitude) decreases What happens to F if q 1 changes sign ( + - )? The direction of is reversed F G F (magnitude) increases What happens to F if r increases? The force from 1 acting on 2 12 2 12 2 1 0 12 ˆ 4 1 r r q q F πε = G Note that the force from 1 acting on 2 equals the force from 2 acting on 1 (Newton’s 3 rd Law) Lecture 2 Page 6 Question 1 Q 2 Q 1 g d 12 Q 2 d 23 To be in equilibrium, the total force on Q 2 must be zero. Two forces acting on Q 2 , gravity , acting down, and the electric force. Therefore, in both cases, the electrical force on Q 2 must be directed upward to cancel its weight. Therefore, the sign of Q 3 must be the SAME as the sign of Q 1 Q 3 A charged ball Q 1 is fixed to a horizontal surface as shown. When another massive charged ball Q 2 is brought near, it achieves an equilibrium position at a distance d 12 directly above Q 1 .
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