1) Magnetic Moment in terms of magnetic poles:
According to Wikipedia, " Magnetic poles always come in pairs, their forces partially cancel each other because while one pole pulls, the other repels. This cancellation is greatest when the poles are close to each other i.e. when the bar magnet is short."
My interpretation: Since 'the cancellation is greatest when the poles are close to each other', practically no force will be experienced when the the distance between the poles tend to zero. Therefore, no field lines will emerge, correct? (Though I know there is something terribly wrong with this)
2) Magnetic Dipole as limit of current carrying loop:
"A magnetic dipole is an idealized current loop - where area goes to zero and current to infinity so that their product is finite. The closer you approximate this situation, the more the field starts to look like a dipole field - analogous with the field created when you approach a positive and negative charge closer and closer together, with the product of charge and distance (the dipole moment) constant."
(a) Why area zero and current infinity? What good is that?
(b) When positive and negative charges approach each other, the distance between them changes. So, how can the product of charge and distance be constant ?
(c) This image again contradicts my interpretation of Magnetic Dipole Moment.