Do mass and charge always go hand in hand for magnetism?

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Tony Stark
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Is it necessary -
1. to have mass for having a charge?
2. to have charge in order to magnetic property?
 
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Re: 2. A neutron is electrically neutral and has a magnetic moment. However it has quarks that are charged. So I don't know if you are limiting your question to fundamental particles or are considering composite particles also.