SME
Grade 11 Science · Problem type
The force on a current in a magnetic field
Use this for “A 0.25 m wire carrying 5 A crosses a 0.40 T field at 90°. What force acts on it? What if the angle is 30°?”
Diagram
F = BIL sin θ
F = 0.4 × 5 × 0.25 × sin 90° = 0.5 N
Right-hand rule: fingers along the current, curl them toward B; the thumb points along the force.
With B along the paper the force comes straight out of it or into it.
This is an example. Type your own values to start a new problem.
F (N)
=
B (T)
×
I (A)
×
L (m)
×
sin(
θ
°)
Formulas
F
=
B
×
I
×
L
×
sin(
θ
)
0.5 = 0.4 × 5 × 0.25 × sin(90°)
Assumptions
•
A current in a magnetic field feels F = BIL sin θ, θ the angle between the wire and the field.
•
The force is greatest at 90° and zero along the field; its direction comes from the right-hand rule.
•
This push on a current is what turns an electric motor.
•
From F alone, θ and 180° − θ give the same force: the steps give the angle under 90°.
Step-by-step
WE KNOW
B = 0.4 T, I = 5 A, L = 0.25 m, θ = 90°
FIND
force (F)
Step 1 · Find force (F)
Use F = B × I × L × sin(θ)
Multiply
the
field,
current,
length
and
sin
θ
.
F
=
0.4
×
5
×
0.25
×
sin(90°)
F
=
0.4
×
5
×
0.25
F
=
2
×
0.25
F
=
0.5
N
Check
Put the numbers back in. Both sides should match.
0.5 = 0.4 × 5 × 0.25 × sin(90°) ✓
Topic check
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