To determine the magnitude of the force acting on the wire due to the magnetic field, we can use the formula for the magnetic force on a current-carrying conductor. The equation is given by:
Magnetic Force Formula
The force (F) on a wire carrying current (I) in a magnetic field (B) is calculated using the formula:
F = I × B × L × sin(θ)
- F is the magnetic force in newtons (N).
- I is the current in amperes (A).
- B is the magnetic field strength in teslas (T).
- L is the length of the wire in the magnetic field in meters (m).
- θ is the angle between the direction of the current and the magnetic field.
Given Values
From the problem, we have:
- Magnetic field strength, B = 1.5 T
- Current, I = 7 A
- Radius of the cylindrical region, r = 10 cm = 0.1 m
Determining the Length of the Wire
Since the wire passes through the cylindrical region, we need to determine the length of the wire that is within the magnetic field. Assuming the wire intersects the axis of the cylinder, the length of the wire (L) can be approximated as the diameter of the cylinder:
L = 2 × r = 2 × 0.1 m = 0.2 m
Calculating the Angle
The direction of the current is from north to south, while the magnetic field is directed from east to west. This means that the angle (θ) between the current and the magnetic field is 90 degrees. The sine of 90 degrees is 1:
sin(θ) = sin(90°) = 1
Plugging in the Values
Now we can substitute the values into the formula:
F = I × B × L × sin(θ)
F = 7 A × 1.5 T × 0.2 m × 1
F = 7 × 1.5 × 0.2 = 2.1 N
Final Result
The magnitude of the force acting on the wire is 2.1 N. Therefore, the correct answer is option 1) 2.1 N.
