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Figure 1 shows an experiment to measure the charge of the electron - AQA - A-Level Physics - Question 1 - 2019 - Paper 7
Question 1
Figure 1 shows an experiment to measure the charge of the electron. Negatively charged oil droplets are sprayed from the atomiser into the gap between the two horiz... show full transcript
Worked Solution & Example Answer:Figure 1 shows an experiment to measure the charge of the electron - AQA - A-Level Physics - Question 1 - 2019 - Paper 7
Step 1
Identify the forces acting on the stationary droplet.
Answer
The stationary droplet experiences two primary forces: the weight (gravitational force) acting downwards and the electric (electrostatic) force acting upwards due to the potential difference between the plates. Both forces are equal in magnitude but act in opposite directions. This balance results in a net force of zero, allowing the droplet to remain stationary.
Step 2
Show that the radius of the droplet is about 1 × 10⁻⁶ m.
Answer
To find the radius of the droplet, we use the equation for terminal velocity, where the gravitational force is balanced by the viscous drag force. The gravitational force is:
ho V g = ho \left( \frac{4}{3} \pi r^3 \right) g$$ The viscous drag force is given by: $$F_d = 6 \\pi r \\eta v$$ Setting these equal at terminal velocity (where the droplet falls at 1.0 × 10⁻¹ m s⁻¹) gives: $$\rho \left( \frac{4}{3} \pi r^3 \right) g = 6 \\pi r \\eta v$$ Substituting the values: - Density ($\rho$) = 880 kg m⁻³ - Viscosity ($\eta$) = 1.8 × 10⁻² N s m⁻² - Gravitational acceleration ($g$) = 9.81 m s⁻² - Velocity ($v$) = 1.0 × 10⁻¹ m s⁻¹ Upon solving for $r$, we find: $$r = 1 × 10⁻⁶ m$$Step 3
Deduce whether this suggestion is correct.
Answer
When the droplet splits into two equal-sized spheres, the charge on each sphere would be half of the original droplet's charge, resulting in a charge of −2.4 × 10⁻¹⁹ C per sphere. However, with reduced radius, the gravitational force acting on each sphere decreases more than the electrostatic repulsion potential that arises from having charges on them. Consequently, the forces acting on each smaller sphere would not balance out in the same manner as the original droplet, causing them to not remain stationary. Therefore, the student's suggestion is incorrect.