Given data:
- Length of the conducting rod (l) = 2m
- Current through the rod (I) = 5 Ampere (A)
- Magnetic field of the Earth (B) = 0.6 × 10^-4 Tesla (T)
- Angle of dip (θ) = 30 degrees

To find:
- Direction and magnitude of the magnetic force acting on the rod

Explanation:
1. Magnetic Field:
The Earth has a magnetic field that can be represented by a vector quantity called the magnetic field vector (B). The magnetic field vector has both magnitude and direction. The magnitude of the Earth's magnetic field is given as 0.6 × 10^-4 T.

2. Angle of Dip:
The angle of dip (θ) is the angle made by the Earth's magnetic field with the horizontal plane at a particular location. In this case, the angle of dip is given as 30 degrees.

3. Magnetic Force on a Current-Carrying Conductor:
When a current-carrying conductor is placed in a magnetic field, it experiences a magnetic force. The direction of the magnetic force can be determined using Fleming's left-hand rule. According to the rule, if the thumb, forefinger, and middle finger of the left hand are held mutually perpendicular to each other, then the thumb points in the direction of motion, the forefinger points in the direction of the magnetic field, and the middle finger points in the direction of the magnetic force.

4. Direction of Magnetic Force:
In this case, the current is flowing from south to north along the conducting rod. Therefore, the magnetic force will act perpendicular to both the direction of the current and the magnetic field.

Since the rod is placed in the north-south direction, the magnetic field due to the Earth will be acting in the vertical plane. The angle of dip tells us how much the magnetic field deviates from the vertical plane. In this case, the angle of dip is 30 degrees, which means that the magnetic field makes an angle of 30 degrees with the horizontal plane.

5. Calculation of Magnetic Force:
The magnitude of the magnetic force acting on the rod can be calculated using the formula:
F = B * l * I * sin(θ)

Where:
F is the magnetic force
B is the magnetic field
l is the length of the conductor
I is the current flowing through the conductor
θ is the angle of dip

Substituting the given values:
F = (0.6 × 10^-4 T) * (2m) * (5 A) * sin(30 degrees)

Simplifying the expression:
F = (0.6 × 10^-4 T) * (2m) * (5 A) * (0.5)

F = 0.6 × 10^-4 * 2 * 5 * 0.5

F = 0.6 × 10^-4 * 1 * 0.5

F = 0.3 × 10^-4 N

Therefore, the magnitude of the magnetic force acting on the rod is 0.3 × 10^-4 N.

6. Direction of Magnetic Force:
As mentioned earlier, the direction of the magnetic force