To find the force per unit length on a straight conductor carrying a current in a magnetic field, we can use the formula derived from the Lorentz force law. The force \( F \) on a conductor of length \( L \) carrying a current \( I \) in a magnetic field \( B \) is given by:
Formula for Magnetic Force
The formula for the magnetic force per unit length \( f \) is expressed as:
f = B \cdot I \cdot \sin(\theta)
Where:
- f = force per unit length (N/m)
- B = magnetic field strength (T)
- I = current (A)
- θ = angle between the direction of the magnetic field and the direction of the current (degrees)
Given Values
In this scenario:
- The magnetic field strength \( B = 3 \times 10^{-5} \, \text{T} \)
- The current \( I = 1 \, \text{A} \)
- The direction of the magnetic field is from geographic south to geographic north.
- The current flows from east to west.
Determining the Angle
Since the magnetic field is directed from south to north and the current is directed from east to west, the angle \( θ \) between the magnetic field and the current direction is \( 90^\circ \). The sine of \( 90^\circ \) is 1, which simplifies our calculations:
sin(θ) = sin(90°) = 1
Calculating the Force per Unit Length
Now we can substitute the values into the formula:
f = B \cdot I \cdot sin(θ)
Substituting the known values:
f = (3 \times 10^{-5} \, \text{T}) \cdot (1 \, \text{A}) \cdot (1)
f = 3 \times 10^{-5} \, \text{N/m}
Direction of the Force
To determine the direction of the force, we can use the right-hand rule. Point your thumb in the direction of the current (east to west) and your fingers in the direction of the magnetic field (south to north). Your palm will then face upwards, indicating that the force on the conductor is directed upwards.
Summary
The force per unit length on the conductor is 3 x 10^-5 N/m, and the direction of the force is upwards.
