I have no idea on the first. THe term third right-hand rule must be unique to your text.
On the second, it depends on what kind of charges you are discussing: positive, or negative. Wouldn't that matter?
1)The direction of the force on doubly ionized helium atoms(alpha particles)moving at right angles to a magnetic field is opposite to the direction of the force given by the third right-hand rule.
true.
2)The electromotive force is a force that makes charges flow from a point of higher potential to lower potential.
false. from low to high
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