Current passing through a conductor is increased from 10 A to 15 A. This decreases the strength of the magnetic field produced by the conductor.

True

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.

False

An increase in current produces a stronger magnetic field.

I don't know what the third right hand rule is.

To determine the answer to the first statement, we need to understand the relationship between the current passing through a conductor and the strength of the magnetic field it produces. According to Ampere's law, the magnetic field produced by a current-carrying conductor is directly proportional to the current flowing through it.

Therefore, when the current passing through a conductor is increased, the strength of the magnetic field produced also increases. In this case, the current is being increased from 10 A to 15 A, which means the magnetic field will also increase.

So, the statement "Current passing through a conductor is increased from 10 A to 15 A. This decreases the strength of the magnetic field produced by the conductor" is False.

Moving on to the second statement, the third right-hand rule is used to determine the direction of the force on a charged particle moving in a magnetic field. According to this rule, if the thumb points in the direction of the velocity of the charged particle, and the fingers point in the direction of the magnetic field, the force is experienced in the direction perpendicular to both thumb and fingers.

For doubly ionized helium atoms (alpha particles), which have positive charge, moving at right angles to a magnetic field, the force experienced will be in the direction determined by the third right-hand rule, opposite to the force experienced by negatively charged particles.

Therefore, the statement "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" is True.