Why only Earth has a magnetic field around it and not other planets?
Other planets do have magnetic fields.
and in the case of Jupiter the magnetic field is strong enough that it causes radio frequency emission which we can detect.
And why do these planets show magnetism?
I'm sorry I don't understand your question. Are you asking why they have magnetic fields? As in, what generates the magnetic fields?
They have magnetic fields for the same or similar reasons that earth does
Read those links that Drakkith gave you .... they give you your answers
Earth is however the only one of the inner rocky planets which has a significant magnetic field.
Mars seems to have remnants of a magnetic field in the past, but probably it doesn't have a liquid metal core any more.
Mercury likely never had one for any length of time as it's very small.
Venus though is anomalous, but then again it's anomalous in other ways, mainly in that it rotates 'backwards' around it's axis in relation to the other planets, (although that rotation is very slow.)
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