FL =B I ℓ (B ┴ I )
- FL magnetic force (or Lorentz force) in N
- B magnetic induction in T (Tesla) 1 T = 1 N A-1 m-1
- I current in A
- ℓ length of the wire in the magnetic field
Example 1
A long straight wire is in a uniform magnetic field
The electric current is 3.0 A
B = 5.0 x 10-2 T
What is the magnitude of the magnetic force in the two situations below and what direction has this force?
Situation 1
B is parallel to I : magnetic force FL = 0 N
Situation 2
FL = BIℓ
FL = (5.0 x 10-2)(.3.0)( 0.40) = 0.06 N
Find direction with for example using the Left-Hand- Rule
- catch the field lines on the palm of your left hand
- fingers in the direction of I
- thumb gives the direction magnetic force F
- FL is perpendicular to B and I
- In this example : F is perpendicular to the plane of the paper and points to you. This is indicated by a dot.
Example 2
Find the magnetic force in the next situation:
- B = 0.20 T
- I = 4.0 A
- ℓ = 25 cm (length wire in magnetic field)
- α = 40 o
Resolve the vector I into two components .
One component parallel to the vector B and the other component (I’) perpendicular to B.
sin α = I’/I
I ‘= I x sin α
The formula to calculate the magnetic force :
FL = B I’ℓ = B I x sin α ℓ = (0.20)( 4.0 x sin 40o)( 0.25) = 0.13 N
Remark : One can also resolve B into two components parallel and perpendicular to I. Then use the component perpendicular to I.