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Electricity & Magnetism Lecture 4: Coulombs Law

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Summary: Lecture 3 Newtons Laws of motion –1. if F = 0, a = 0 –2. F = m a (N.B. F, a are vectors) –3. F 12 =-F 21 Vectors –Vectors & Scalars –Vector addition Geometric –Unit vectors –Vector components & addition of components Units

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Todays Topics Coulombs Law Vector form of Coulombs Law Coulomb vs Newton Superposition

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Coulombs Law

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Coulomb's Torsion Balance This dial allows you to adjust and measure the torque in the fibre and thus the force restraining the charge This scale allows you to read the separation of the charges

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Coulombs Experiments F r Line F r -2

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Coulomb's Law Coulomb determined –Force is attractive if charges are opposite sign –Force proportional to the product of the charges q 1 and q 2 along the lines joing them –Force inversly proportional square of the distance I.e. –|F 12 | |Q 1 | |Q 2 | / r 12 2 –or –|F 12 |= k |Q 1 | |Q 2 | / r 12 2

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Coulomb's Law Units of constant can be determined from Coulomb's Law Colomb (and others since) have determined this constant which (in a vacuum) in SI units is –k = x10 9 Nm 2 C -2 k is normally expressed as k = 1/4 0 –where is the permittivity of free space

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Coulomb's Law

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Vector form of Coulombs Law ++ Q1 Q2 r

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Quiz A: F AB =-3F BA B: F AB =-F BA C: 3F AB =-F BA D: F AB =12F BA Object A has a charge of +2 C and Object B has a charge of +6 C. Which statement is true? B +6 C A +2 C F AB ?F BA ?

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Force from many charges Superposition

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Force from many charges + Q1 - Q2 + Q4 - Q3 Force on charge is vector sum of forces from all charges Principle of superposition

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Coulomb vs Newton

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Always attractive 1/r 2 very weak important on very large scales, planets, the Universe Coulombs Law vs Newtons Law of Gravity Attractive or repulsive 1/r 2 very strong only relevant relatively local scales Two spheres

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Summary: Lecture 4 Coulomb's Law –Electrostatic Force between charges Coulombs Law (vector) form Coulomb force vs Gravity –Electrostatic force is in general much stronger Superposition

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