The correct answer is option 1: the magnetic field strength of a current carrying wire at a particular distance from the axis of the wire depends upon the current in the wire.

When a current flows through a wire, it creates a magnetic field around the wire. The strength of this magnetic field determines how much force it can exert on other magnetic materials or charged particles in its vicinity. The greater the current passing through the wire, the stronger the magnetic field will be.

Option 2, the radius of the wire, does not directly affect the magnetic field strength. The size or shape of the wire itself does not influence the magnetic field, only the current flowing through it.

Option 3, the temperature of the surroundings, also does not impact the magnetic field strength. The magnetic field is solely determined by the current flowing through the wire and is independent of the temperature.

Therefore, the correct answer is option 1 as the magnetic field strength of a current carrying wire at a particular distance from the axis of the wire depends on the current flowing through the wire.