Unreasonable Results A frazzled theoretical physicist reckons that all conservation laws are obeyed in the decay of a proton into a neutron, positron, and neutrino (as in + decay of a nucleus) and sends a paper to a journal to announce the reaction as a possible end of the universe due to the spontaneous decay of protons. (a) What energy is released in this decay? (b) What is unreasonable about this result? (c) What assumption is responsible?

Lecture 6 Recall E = −∇V ∆V E = − ∆x U = qV Potential from a point charge q V = k r Potential from a distribution of charges 1 qi V = 4π r 0 i i Smooth distribution V = 1 qi= 1 ρdV 4π0 ri 4π0 r i Calculating the electric potential from a group of point charges is usually much simpler than calculating the electric field •It’s a scalar Potential from a distribution of charges 1 qi Just add V = 4π r 0 i i Smooth distribution V = 1 qi = 1 ρdV 4π 0 ri 4π0 r i Calculating the electric potential from a group of point charges is usually much simpler than calculating the electric field •It’s a scalar First calculate , then E E = −∇V dφ ake section dφ dφ Its charge dq = Q 2π Q V = k√ R + z 2 Qz Q Ez= −∂ Vz= k 2 2 3/