Linear Charge Density Converter - Convert C/m, μC/cm, nC/mm & More Units
Result:
1 C/m = 1.000000e+4 μC/cm
What is Linear Charge Density?
Simple Definition
Linear charge density tells us how much electric charge is spread along a line or wire. It shows the amount of charge per unit length.
Think of it like counting beads on a string - how many beads per inch?
Common Units
• C/m (Coulomb per meter) - Base unit
• μC/cm (Microcoulomb per centimeter)
• nC/mm (Nanocoulomb per millimeter)
• pC/μm (Picocoulomb per micrometer)
How Linear Charge Density Conversion Works
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Linear Charge Density Formulas
Basic Formula:
λ = Q / L
Where λ = linear charge density, Q = total charge, L = length
Unit Conversion:
λ₂ = λ₁ × (f₁/f₂)
Where f₁, f₂ are conversion factors to base unit
Example Calculation:
Convert 5 μC/cm to C/m:
5 × 0.0001 = 0.0005 C/m
Electric Field:
E = λ / (2πε₀r)
Electric field from infinite line charge
Linear Charge Density Conversion Table
| C/m | μC/cm | nC/mm | pC/μm | C/cm | mC/m |
|---|---|---|---|---|---|
| 1.00e-9 | 1.00e-5 | 1.00e-3 | 1.00e-3 | 1.00e-11 | 1.00e-6 |
| 1.00e-8 | 1.00e-4 | 1.00e-2 | 1.00e-2 | 1.00e-10 | 1.00e-5 |
| 1.00e-7 | 1.00e-3 | 1.00e-1 | 1.00e-1 | 1.00e-9 | 1.00e-4 |
| 1.00e-6 | 1.00e-2 | 1.00e+0 | 1.00e+0 | 1.00e-8 | 1.00e-3 |
| 1.00e-5 | 1.00e-1 | 1.00e+1 | 1.00e+1 | 1.00e-7 | 1.00e-2 |
| 1.00e-4 | 1.00e+0 | 1.00e+2 | 1.00e+2 | 1.00e-6 | 1.00e-1 |
| 1.00e-3 | 1.00e+1 | 1.00e+3 | 1.00e+3 | 1.00e-5 | 1.00e+0 |
| 1.00e-2 | 1.00e+2 | 1.00e+4 | 1.00e+4 | 1.00e-4 | 1.00e+1 |
| 1.00e-1 | 1.00e+3 | 1.00e+5 | 1.00e+5 | 1.00e-3 | 1.00e+2 |
| 1.00e+0 | 1.00e+4 | 1.00e+6 | 1.00e+6 | 1.00e-2 | 1.00e+3 |
| 1.00e+1 | 1.00e+5 | 1.00e+7 | 1.00e+7 | 1.00e-1 | 1.00e+4 |
| 1.00e+2 | 1.00e+6 | 1.00e+8 | 1.00e+8 | 1.00e+0 | 1.00e+5 |
| 1.00e+3 | 1.00e+7 | 1.00e+9 | 1.00e+9 | 1.00e+1 | 1.00e+6 |
| 1.00e+4 | 1.00e+8 | 1.00e+10 | 1.00e+10 | 1.00e+2 | 1.00e+7 |
| 1.00e+5 | 1.00e+9 | 1.00e+11 | 1.00e+11 | 1.00e+3 | 1.00e+8 |
Linear Charge Density Units Progression Chart
1 C/m
0.1 C/m
0.01 C/m
0.001 C/m
0.0001 C/m
0.00001 C/m
Step by Step Examples
Example 1: Convert 25 μC/cm to C/m
Step 1: Know that 1 μC/cm = 0.0001 C/m
Step 2: Multiply 25 × 0.0001
Answer: 0.0025 C/m
Example 2: Convert 0.5 C/m to nC/mm
Step 1: Know that 1 C/m = 1,000,000 nC/mm
Step 2: Multiply 0.5 × 1,000,000
Answer: 500,000 nC/mm
Example 3: Find charge density
A wire has 0.001 C charge in 2 cm length
Step 1: Divide charge by length
Step 2: 0.001 C ÷ 2 cm = 0.0005 C/cm
Answer: 0.0005 C/cm or 5 μC/cm
Example 4: Convert 100 pC/μm to μC/cm
Step 1: Convert pC to μC: 100 pC = 0.0001 μC
Step 2: Convert μm to cm: 1 μm = 0.0001 cm
Step 3: 0.0001 μC ÷ 0.0001 cm
Answer: 1 μC/cm
Frequently Asked Questions
What is linear charge density?
It measures how much electric charge is spread along a line or wire. Like counting how many coins are in each meter of a long line.
Why do we need different units?
Different situations need different scales. Tiny wires use small units like pC/μm, while power lines use larger units like C/m.
How accurate is this converter?
Very accurate! We use exact conversion factors based on scientific standards. Perfect for homework and real work.
Can I use this for homework?
Yes! This tool helps you check your work and learn the conversion process. Always show your work steps too.
What's the most common unit?
C/m is the base unit in science. But μC/cm and nC/mm are popular for smaller measurements in labs and electronics.
Is linear charge density dangerous?
The numbers themselves are safe. But high charge density on real wires can be dangerous. Always follow safety rules with electricity.
Common Examples of Linear Charge Density
Real World Examples
• Power lines: 10⁻⁶ to 10⁻⁵ C/m
• TV antenna: 10⁻⁹ to 10⁻⁸ C/m
• Lightning rod: 10⁻⁷ to 10⁻⁶ C/m
• Phone cable: 10⁻¹⁰ to 10⁻⁹ C/m
Lab Examples
• Charged rod: 1 μC/cm
• Wire in experiment: 10 nC/mm
• Thin fiber: 100 pC/μm
• Test wire: 0.1 mC/m
Where We Use Linear Charge Density
Power Lines
Electric wires carry charge along their length
TV Cables
Coax cables have charge spread on inner wire
Lightning Rods
Metal rods collect charge from air
Phone Lines
Telephone wires carry small charges
Lab Equipment
Science tools use charged wires
Antennas
Radio antennas have charge distribution