SME
Grade 11 Science · Physics
Static electricity: charge, Coulomb's law and electric fields
Use this for “A +3 μC and a −5 μC charge sit 0.2 m apart. How strong is the force, and does it attract or repel?”
Diagram
F
=
k|q₁q₂|/
r
2
F
=
8.99 ×
10
9
×
3 ×
10
-6
×
5 ×
10
-6
/
0.2
2
F = 3.37 N
Unlike charges attract: each is pulled toward the other, just as hard.
Field lines leave + charges and end on − charges; where they crowd, the field is strong.
This is an example. Type your own values to start a new problem.
F (N)
=
8.99
×
10⁹
×
q₁ (μC)
×
(
q₂ (μC)
)
(
r (m)
)
2
Formulas
F
=
8.99 ×
10
9
×
q₁
×
10
-6
×
q₂
×
10
-6
/(
r
2
)
−3.37
=
8.99 ×
10
9
×
3 ×
10
-6
×
(−5)
×
10
-6
/(
0.2
2
)
Assumptions
•
Point charges: each is small next to the distance r between them.
•
Like charges repel (F > 0); unlike charges attract (F < 0). 1 μC = 10⁻⁶ C.
•
F = kq₁q₂/r² with k = 8.99 × 10⁹ N·m²/C²: doubling r gives a quarter of the force.
Step-by-step
WE KNOW
q₁ = 3 μC, q₂ = −5 μC, r = 0.2 m
FIND
force (F)
Step 1 · Find force (F)
Use F = 8.99 × 10⁹ × q₁ × 10⁻⁶ × q₂ × 10⁻⁶/(r²)
Coulomb’s
law:
k
=
8.99 ×
10
9
N·
m
2
/
C
2
times
the
two
charges
in
coulombs
(1
μC
=
10
-6
C),
over
r
2
.
F
=
8.99 ×
10
9
×
3 ×
10
-6
×
(−5)
×
10
-6
/(
0.2
2
)
q₁
×
q₂
=
(3
×
10
-6
)
×
(−5
×
10
-6
)
=
−1.5 ×
10
-11
C
2
r
2
=
(0.2)
2
=
0.04
m²
F
=
8.99 ×
10
9
×
(−1.5
×
10
-11
)/0.04
F
=
−3.37
N
Check
Put the numbers back in. Both sides should match.
−3.37
≈
8.99 ×
10
9
×
3 ×
10
-6
×
(−5)
×
10
-6
/(
0.2
2
)
✓
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