$(a)$ Magnetic field lines of two bar magnets $A$ and $B$ are as shown below. Name the poles of the magnets facing each other.
$(b)$ Two magnetic field lines never intersect each other. Why?
$(c)$ How does the strength of the magnetic field at the centre of a current-carrying circular coil depend on the
$(i)$ radius of the coil,
$(ii)$ number of turns in the coil, and
$(iii)$ strength of the current flowing in the coil?

(N/A) The magnetic field lines are shown moving away from the poles of both magnets $A$ and $B$. Since magnetic field lines emerge from the North pole, the poles facing each other are both North poles.
$(b)$ Two magnetic field lines never intersect each other because if they did, the point of intersection would have two different directions for the magnetic field at the same time, which is physically impossible.
$(c)$ The strength of the magnetic field at the centre of a current-carrying circular coil depends on the following factors:
$(i)$ Radius of the coil: The magnetic field strength is inversely proportional to the radius of the coil $(B \propto 1/r)$. Thus, a larger radius results in a weaker magnetic field.
$(ii)$ Number of turns in the coil: The magnetic field strength is directly proportional to the number of turns $(B \propto n)$. Increasing the number of turns increases the magnetic field strength.
$(iii)$ Strength of the current: The magnetic field strength is directly proportional to the current flowing through the coil $(B \propto I)$. Increasing the current increases the magnetic field strength.