Physics Lab How To Calculate Charge Of Wand With Mylar

Estimate the charge transferred from a rubbed wand to two identical mylar strips using force balance and Coulomb’s law. This is ideal for electrostatics labs that use repelling mylar vanes or lightweight foil strips.

Model used: for each strip, Fe = mg tan(theta), and q = sqrt(Fe r² / k) where r is the separation between strips.

Expert Guide: Physics Lab How to Calculate Charge of Wand with Mylar

Measuring electrostatic charge in a classroom or introductory university lab often feels mysterious because the quantities are so small, the objects are lightweight, and environmental conditions matter. A mylar-strip setup gives you a practical way to estimate charge using visible motion. If a charged wand touches or transfers charge to two identical hanging mylar strips, the strips repel. That repulsion reveals the electric force, and from that force you can estimate the amount of charge.

What the mylar method is actually measuring

When a rubbed plastic wand, PVC rod, acrylic rod, or similar insulator transfers charge to two suspended mylar strips, the strips usually end up with the same sign of charge. Since like charges repel, each strip swings outward until the sideways electric force is balanced by the sideways component of tension in the support. At equilibrium, three forces matter on each strip:

• Weight downward, equal to mg
• Tension along the strip support line
• Electrostatic repulsion horizontally from the other strip

That means your measurement of separation is not just a visual effect. It is a force measurement in disguise. Once you know the force, you can use Coulomb’s law to solve for charge.

Core equations

1. Geometry: if the strips have length L and the center-to-center separation is r, then each strip is displaced by r/2.

2. Angle from vertical: sin(theta) = (r/2) / L

3. Force balance: Fe = mg tan(theta)

4. Coulomb’s law for equal strip charges: Fe = k q² / r²

5. Solve for charge on each strip: q = sqrt(Fe r² / k)

If you assume the wand transferred most of its charge to the two strips, then the wand charge magnitude is approximately the total strip charge, or about 2q. In many real labs, transfer is not perfect, so an efficiency estimate helps. For example, if you think only 80% of the wand’s charge ended up on the strips, then the estimated initial wand charge is 2q / 0.80.

Why mylar is used in electrostatics labs

Mylar, which is a form of PET polyester film, works well because it is lightweight, smooth, durable, and easy to cut into uniform strips. Since the strips have very small mass, even tiny electric forces can cause measurable deflection. Mylar also resists tearing better than some thin paper alternatives, making repeated trial runs more consistent.

Constant or material property	Typical value	Why it matters in the lab
Coulomb constant, k	8.9875 × 10^9 N·m²/C²	Used directly to convert measured force and separation into charge.
Standard gravitational acceleration, g	9.80665 m/s²	Needed to compute the strip weight and the balancing force.
PET density	About 1.38 to 1.40 g/cm³	Useful if you need to estimate strip mass from dimensions instead of weighing it.
Dielectric constant of PET	About 3.0 to 3.3	Explains why mylar can hold charge locally and behave differently from a conductor.
Breakdown strength of dry air	About 3 × 10^6 V/m	Shows why very strong fields can discharge suddenly through air.

These values are representative and align with standard references used in physics and materials science. In a typical school lab, the charge on each strip is often in the nanocoulomb to low microcoulomb range, depending on humidity, surface contamination, and the material rubbed against the wand.

Step by step: how to calculate the charge of the wand

1. Prepare two identical strips. Make sure they have the same length and approximately the same mass. Uniform strips help justify the equal-charge model.
2. Measure the strip length. Use the hanging length from the support point to the center of mass or center of the charged region. In many simple labs, using the full hanging length is a good approximation.
3. Measure the mass of each strip. If you have a milligram balance, use it. If not, estimate from area, thickness, and PET density, but expect more uncertainty.
4. Charge the wand. Rub the wand with the prescribed material such as wool, fur, or paper towel according to your lab instructions.
5. Transfer charge. Touch the wand to the strips or use the lab’s specific charging procedure.
6. Measure the final separation. Wait until the strips settle. Measure the distance between the centers of the two strips, not edge to edge unless your lab explicitly uses edge separation.
7. Compute the angle. Use the strip length and half of the separation to find the deflection angle.
8. Compute electrostatic force. Use Fe = mg tan(theta).
9. Solve for strip charge. Use Coulomb’s law for equal charges to find q.
10. Estimate wand charge. Add the two strip charges and correct for any expected transfer efficiency.

Worked example

Suppose each mylar strip is 5.0 cm long and has mass 5.0 mg. After charging, the strip centers are 20.0 mm apart.

• L = 0.050 m
• m = 5.0 mg = 5.0 × 10^-6 kg
• r = 20.0 mm = 0.020 m

Each strip is displaced horizontally by r/2 = 0.010 m. The angle satisfies:

sin(theta) = 0.010 / 0.050 = 0.20

So theta ≈ 11.54 degrees. Then:

Fe = mg tan(theta)

Fe ≈ (5.0 × 10^-6)(9.80665)(tan 11.54 degrees)

Fe ≈ 1.00 × 10^-5 N

Now use Coulomb’s law:

q = sqrt(Fe r² / k)

q ≈ sqrt((1.00 × 10^-5)(0.020)² / (8.9875 × 10⁹))

q ≈ 6.67 × 10^-10 C

That is about 0.667 nC per strip. If you assume both strips together represent 80% of the original wand charge, then the estimated initial wand charge is:

Qwand ≈ 2q / 0.80 ≈ 1.67 nC

Quick interpretation: Small separations usually correspond to sub-nanocoulomb strip charges for very light strips. Much larger separations or lighter strips can produce values several times larger.

Comparison table for common lab outcomes

The following example set uses the same strip length of 5.0 cm and mass of 5.0 mg, then compares how observed separation changes the estimated strip charge. This is helpful when checking whether your answer is in a realistic range.

Observed separation r	Angle from vertical	Electrostatic force on each strip	Estimated charge on each strip	Total charge on two strips
10 mm	5.74 degrees	4.92 × 10^-6 N	0.234 nC	0.468 nC
20 mm	11.54 degrees	1.00 × 10^-5 N	0.667 nC	1.334 nC
30 mm	17.46 degrees	1.54 × 10^-5 N	1.276 nC	2.552 nC
40 mm	23.58 degrees	2.14 × 10^-5 N	1.952 nC	3.904 nC

Notice that the estimated charge rises faster than the separation alone might suggest, because both the force balance and Coulomb relation contribute. This is why careful measurement of spacing is so important.

Most common sources of error

• Humidity: Moist air allows charges to leak away more quickly. A dry room usually gives stronger and more repeatable results.
• Mass uncertainty: Since the force depends on weight, a poor mass estimate directly affects the final charge calculation.
• Separation measured at the wrong point: Edge-to-edge and center-to-center distances are not the same. Your formula assumes center-to-center distance.
• Non-identical strips: If one strip is heavier, longer, or more contaminated than the other, equal-charge assumptions become weaker.
• Air currents: Tiny drafts can noticeably move lightweight mylar strips.
• Charge leakage to supports: If the support is slightly conductive or dirty, the strips can lose charge quickly.
• Induction versus transfer confusion: Some labs charge by contact, others by induction. The formula above is most direct when both strips end up carrying equal charge of the same sign.

How to improve accuracy in a school or university lab

1. Use a dark background with a millimeter scale behind the strips.
2. Take a photo straight on and measure separation from the image to reduce parallax.
3. Repeat at least 5 trials and average the separation.
4. Handle the strips with gloves or tweezers to avoid contamination and charge leakage.
5. Measure mass on a balance rather than estimating from dimensions whenever possible.
6. Keep the support geometry fixed so the strip length is consistent from trial to trial.
7. Record room humidity if your lab wants higher-quality uncertainty analysis.

When this calculation is valid and when it is only an estimate

This method is best treated as an estimate, not an exact metrology technique. Coulomb’s law assumes point charges, while mylar strips have charge distributed over an area. The strips can also polarize and twist, so the effective charge location may not sit exactly at the geometric center. Even so, the model is excellent for demonstrating the connection between observable motion and electric force.

In introductory electrostatics, the educational value is huge. Students see how a simple hanging system converts an invisible electric effect into measurable geometry. They also confront model assumptions, uncertainty, and the challenge of approximating real materials with ideal equations.

Authoritative references for deeper study

• NIST Fundamental Physical Constants for the accepted values of Coulomb-related constants and standard physical data.
• NASA Glenn educational resources for clear explanations of force balance and vector components used in equilibrium reasoning.
• Georgia State University HyperPhysics electric force reference for an accessible review of Coulomb’s law concepts.

Bottom line

If your lab asks, “physics lab how to calculate charge of wand with mylar,” the practical answer is this: use the observed separation of the charged mylar strips, convert that separation into a deflection angle, use force balance to find the electric repulsion, and then use Coulomb’s law to solve for charge. The result gives the charge on each strip, and from there you can estimate the original charge on the wand.

The calculator above automates these steps, but the real physics remains simple and elegant. A tiny mass, a measurable angle, and a well-known law let you estimate one of the most elusive quantities in an introductory lab: electrostatic charge.

This calculator is intended for educational use. If your instructor uses a different geometry, edge-to-edge spacing, or a calibration factor based on your apparatus, follow the lab manual first and use this tool as a conceptual or cross-checking aid.