D O C U M E N T 4 8 3 F E B R U A R Y 1 9 2 7 4 8 1 [B is at rest against the fixed-star system, the spheres are rotating against it.] c.) What kind of field will observer B detect if the spheres are rotating at angular velocity ω and the observer is participating in that rotation? [Mutually at rest joint rotation against the fixed-star system.] In my view, the following will occur: Case a.) needs no closer consideration: the observer measures neither an electric nor a magnetic field. For the calculation of case b.) one needs a formula for the magnetic field of a rotating charged sphere. This is easily obtained if one starts from the magnetic potential of a circular electric current. According to Maxwell (-Wein- stein’s translation),[6] volume II, page 412, the mag- netic potential of the circular current E E′ at point B is given by . A spherical zone of the width yields for a charge density σ and an angular velocity ω a current . Hence, The potential coming from the whole sphere is then . By reformulating the integral and applying the integral laws of sphere functions, one finds that from the total sum only the term for n = 1 remains and one gets . From this the horizontal field component results . If one has a sphere with a total charge +e and a radius , then and ω′ 2πsin2α 1 n 1+ ----------- - cn 1+ rn 1+ ----------- Pn′ α) ( Pn( ϑ) ⋅ ⋅ ⋅ n 1= ∞ ¦ = c d α⋅ σ c dα ω c cosα ⋅ ⋅ ⋅ ⋅ ⋅ dV 2πsin2α σ c2 dα ω dα 1 n 1+ ----------- - cn 1+ rn 1+ ----------- Pn′ α) ( Pn(ϑ) ⋅ ⋅ ⋅ n 1= ∞ ¦ ⋅ cosα ⋅ ⋅ ⋅ ⋅ ⋅ = V 2πωσ Pn(ϑ- ) n 1+ -------------- cn 3+ rn 1+ ----------- Pn′ α) ( sin2α cosα ⋅ ⋅ dα) ⋅ ( π 2 -- -– π 2 -+-- ³ ⋅ n 1= ∞ ¦ = V 4 3 --πωσ - c4 r2 ---- - cosϑ ⋅ ⋅ = Hhorizontal –∂V r ϑ∂⋅ ------------- 4 3 --πωσ - c4 r3 ---- - sinϑ ⋅ ⋅ = = a1 σ1 e 4πa12 ------------ =