The discovery of the electron common mistakes

Common mistakes

• Misunderstanding Specific Charge Calculation

  Students often confuse the specific charge formula, leading to incorrect calculations of charge-to-mass ratios.

  Fix itTo calculate specific charge (q/m), use the formula q/m = F / (B^2 * r), where F is the force on the charged particle, B is the magnetic field strength, and r is the radius of the circular path. Substitute the values correctly and ensure units are consistent. For example, if F = 0.02 N, B = 0.1 T, and r = 0.05 m, then q/m = 0.02 / (0.1^2 * 0.05) = 4 C/kg.

• Misunderstanding Specific Charge Calculation

  Students often confuse the specific charge formula, leading to incorrect calculations of the charge-to-mass ratio of the electron.

  Fix itTo correctly calculate specific charge, use the formula specific charge = charge / mass. Substitute the known values for charge and mass, then perform the calculation to find the specific charge in C/kg.

• Misunderstanding the Oil-Drop Experiment

  Students often confuse the principle of Millikan's oil-drop experiment with other experiments, failing to recognize that it measures the charge of an electron by balancing gravitational and electric forces on tiny oil droplets.

  Fix itTo fix this, remember that the experiment involves adjusting the electric field until the oil droplet is suspended, allowing you to calculate the charge using the formula: F_gravity = F_electric. Substitute the known values for mass and electric field strength to find the charge of the electron.

• Misunderstanding Force Balance

  Students often confuse the concept of force balance in Millikan's oil-drop experiment, thinking that the charge can be calculated directly without considering the forces acting on the droplet.

  Fix itTo correctly explain how force balance gives charge values, start with the formula for the forces acting on the droplet: F_gravity = F_electric. Substitute the expressions for these forces: mg = qE, where m is the mass of the droplet, g is the gravitational field strength, q is the charge, and E is the electric field strength. Rearranging gives q = mg/E. Calculate the charge using known values for mass and electric field strength, ensuring to include units (C for charge). This shows the relationship between the forces and the charge of the electron.

• Misunderstanding Quantisation of Charge

  Students often confuse the concept of quantisation of charge with the idea that charge can take on any value, rather than being discrete.

  Fix itTo fix this, students should focus on the evidence from Millikan's oil-drop experiment, which shows that charge exists in fixed amounts (multiples of the elementary charge). They should understand that this implies charge cannot be fractional and conclude that quantisation is a fundamental property of electric charge.

• Linking Electronic Charge

  Students often confuse the specific charge of the electron with its mass, failing to recognize that specific charge is the ratio of charge to mass.

  Fix itTo fix this, remember that specific charge (q/m) is calculated using the formula: specific charge = charge / mass. Substitute the known values for charge and mass, perform the calculation, and ensure to express the specific charge in C/kg.