SME
Grade 11 Science · Problem type
The force on a moving charge
Use this for “A 5 μC charge moves at 400 m/s across a 0.3 T field. What force acts on it? What if it moves at 30° to the field?”
Diagram
F = |q|vB sin θ
F
=
5 ×
10
-6
×
400
×
0.3
×
sin
90°
F
=
6 ×
10
-4
N
Right-hand rule for a + charge: fingers along v, curl them toward B; the thumb is F.
This is an example. Type your own values to start a new problem.
F (N)
=
|
q (μC)
|
×
v (m/s)
×
B (T)
×
sin(
θ
°)
Formulas
F
=
|
q
|
×
10
-6
×
v
×
B
×
sin(
θ
)
6.00 ×
10
-4
=
|5|
×
10
-6
×
400
×
0.3
×
sin(90°)
Assumptions
•
A charge moving through a magnetic field feels F = |q|vB sin θ, θ the angle between v and B.
•
The force is square to both v and B (right-hand rule): a − charge is pushed the other way.
•
A charge moving along the field feels no force.
Step-by-step
WE KNOW
q = 5 μC, v = 400 m/s, B = 0.3 T, θ = 90°
FIND
force (F)
Step 1 · Find force (F)
Use F = |q| × 10⁻⁶ × v × B × sin(θ)
The
charge
in
coulombs
times
the
speed,
the
field
and
sin
θ
.
F
=
q
×
10
-6
×
v
×
B
×
sin(
θ
)
F
=
5 ×
10
-6
×
400
×
0.3
×
sin(90°)
F
=
5 ×
10
-6
×
400
×
0.3
×
1
F
=
6.00 ×
10
-4
N
Check
Put the numbers back in. Both sides should match.
6.00 ×
10
-4
=
|5|
×
10
-6
×
400
×
0.3
×
sin(90°)
✓
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