N.32 More on Maxwell’s third law

Since the volt­age is mi­nus the in­te­gral of the elec­tric field, it might seem that there is a plus and mi­nus mixed up in fig­ure 13.5.

But ac­tu­ally, it is a bit more com­plex. The ini­tial ef­fect of the in­duced elec­tric field is to drive the elec­trons to­wards the pole marked as neg­a­tive. (Re­call that the charge of elec­trons is neg­a­tive, so the force on the elec­trons is in the di­rec­tion op­po­site to the elec­tric field.) The ac­cu­mu­la­tion of elec­trons at the neg­a­tive pole sets up a counter-act­ing elec­tric field that stops fur­ther mo­tion of the elec­trons. Since the leads to the load will be stranded to­gether rather than laid out in a cir­cle, they are not af­fected by the in­duced elec­tric field, but only by the counter-act­ing one. If you want, just for­get about volt­ages and con­sider that the in­duced elec­tric field will force the elec­trons out of the neg­a­tive ter­mi­nal and through the load.