A　magnetic　field　induced　by　an　electromagnetic　coil　is　the　key　variable　that　determines　the　performance　of　a　magnetically　driven　actuator.　The　applicability　of　the　empirical　models　of　the　coil　turns,　static　resistance,　and　inductance　were　discussed.　Then,　the　model　of　the　mean　magnetic　field　induced　by　the　coil　was　established　analytically.　Based　on　the　proposed　model,　the　sinusoidal　response　and　square-wave　response　were　calculated　with　the　wire　diameter　as　the　decision　variable.　The　amplitude　and　phase　lag　of　the　sinusoidal　response,　the　time-domain　response,　steady-state　value,　and　the　response　time　of　the　square-wave　response　were　discussed　under　different　wire　diameters.　From　the　experimental　and　computational　results,　the　model　was　verified　as　the　relative　errors　were　acceptably　low　in　computing　various　responses　and　characteristic　variables.　Additionally,　the　optimization　on　the　wire　diameter　was　carried　out　for　the　optimal　amplitude　and　response　time.　The　proposed　model　will　be　helpful　for　the　analytical　analysis　of　the　mean　magnetic　field,　and　the　optimization　result　of　the　wire　diameter　under　limited　space　can　be　employed　to　improve　the　performance　of　a　magnetically　driven　actuator.　©　2023　by　the　authors.