Why Does the Sun Shine? (E&M??) Coulombs Law including the 1 / r - PowerPoint PPT Presentation

Why Does the Sun Shine? (E&M??) Coulomb’s Law including the 1 / r 2 dependence on the separation 1. Newton’s Law of Universal Gravitation shares many attributes of r r r 2 ˆ r 2 between point particles. qQ F G = − GmM 1 � � F C = ˆ 4 πǫ 0 2. What is the gravitational energy of a sphere of mass M and radius R ? Our Sun has M = 1 . 991 × 10 30 kg and R = 6 . 96 × 10 8 m . 3. The Sun produces about 3 . 86 × 10 26 J/s . If the source of the Sun’s energy is the energy stored in the field, how long would it last? W hy Does the Sun Shine? – p.1/9

Assembling a Charge Distribution Consider the charge distribution shown below. How much work has to done to create it from nothing? q 2 q 3 q 4 q 1 W hy Does the Sun Shine? – p.2/9

Assembling a Charge Distribution Consider the charge distribution shown below. How much work has to done to create it from nothing? q 2 r 23 q 3 r 24 r 13 r 12 r 34 q 4 r 14 q 1 W hy Does the Sun Shine? – p.3/9

Assembling a Charge Distribution Consider the charge distribution shown below. How much work has to done to create it from nothing? q 2 q 3 r 12 r 34 q 4 r 14 q 1 W hy Does the Sun Shine? – p.4/9

Assembling a Charge Distribution Consider the charge distribution shown below. How much work has to done to create it from nothing? q 2 r 23 q 3 r 13 r 12 r 34 q 4 r 14 q 1 W hy Does the Sun Shine? – p.5/9

Assembling a Charge Distribution Consider the charge distribution shown below. How much work has to done to create it from nothing? q 2 r 23 q 3 r 24 r 13 r 12 r 34 q 4 r 14 q 1 W hy Does the Sun Shine? – p.6/9

Energy of a Charge Distribution What is the energy stored in a uniformly charged solid sphere of radius R and charge Q ? Use �� � W = ǫ 0 � V � E · d � E 2 dτ + A 2 V S to calculate the energy. z y x W hy Does the Sun Shine? – p.7/9

Energy of a Charge Distribution W hy Does the Sun Shine? – p.8/9

Why Does the Sun Shine? (E&M??) Coulomb’s Law including the 1 / r 2 dependence on the separation 1. Newton’s Law of Universal Gravitation shares many attributes of r r r 2 ˆ r 2 between point particles. qQ F G = − GmM 1 � � F C = ˆ 4 πǫ 0 2. What is the gravitational energy of a sphere of mass M and radius R ? Our Sun has M = 1 . 991 × 10 30 kg and R = 6 . 96 × 10 8 m . 3. The Sun produces about 3 . 86 × 10 26 J/s . If the source of the Sun’s energy is the energy stored in the field, how long would it last? W hy Does the Sun Shine? – p.9/9