Saved Bookmarks
| 1. |
Show mathematically that the electric field due to a short dipole at a distance 'd' along its axis is twice the value of field at the same distance along the equatorial line. |
|
Answer» Solution :We KNOW that ELECTRIC field at a distance .d.along AXIS of an electric dipole is ` ""E_("axial") = (1)/( 4 PI in _0).(2pd)/((d^(2) -a^(2)) ^(2)) ` and for short dipole `(a lt lt d), ` we have ` ""E_("axial ")=(1)/(4 pi in _0).(2p)/(d^(3)) ` Again electric field at a distance .d. along the equatorial line of dipole is ` "" E_("equatorial ") = ( 1)/(4 pi in _0).(p)/( (d^(2) +a^(2)) ^(3//2)) ` and in case of a short dipole ` ""E_("equatorial") =(1)/(4 pi in _0).(p)/(d^(3)) ` Comparing (i) and (ii)we, have ` (E_("axial") )/(E_("equatorial")) = 2 or E_("axial") =2xx E_("equatorial")) ` |
|