248 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



is no electric charge on the surface of the wire, then the electric 

 field in the neighborhood of the wire is parallel to the wire. The 

 lines of force of the magnetic field, on the other hand, encircle the 

 wire, and therefore the energy streams in towards the wire and on 

 all sides, and is converted into heat in the wire. 



Let R be the resistance of the wire in abohms per centimeter 

 of length, and let / be the current in the wire, in abamperes, 

 then RI is the intensity of the surrounding electric field * in 

 abvolts per centimeter. According to Art. 55, the intensity of 

 the magnetic field at a distance of r centimeters from the wire 

 is 2! r /r gausses. The intensity of the energy stream (units of 

 energy per unit of area per second) at a distance of r centi- 

 meters from the wire is proportional to the product of the elec- 

 tric field and magnetic field intensities, and it may therefore be 

 written kx RI X 2f/r, where k is an unknown proportionality 

 factor. Multiplying this expression for the intensity of the 

 energy stream by the area of a cylindrical surface / centimeters 

 in length and r centimeters in radius (co-axial with the wire), 

 we have the total energy per second streaming in to / centi- 

 meters of the wire, and this must be equal to / x RI*. Therefore, 

 we have 



2wr/x kxRIx =lxRI* 

 r 



whence 



K ^ = 



47T 



Therefore we have 



S-^-Hf (77) 



in which 6" is the energy in ergs per second which streams 

 across one square centimeter of area at right angles to a magnetic 

 field of which the intensity is H gausses and at right angles to 

 an electric field of which the intensity is / abvolts per centi- 

 meter, H and / being at right angles to each other. 



* The intensity of that component of the electric field which is parallel to the wire. 



