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Figure 3 shows an arrangement used to investigate the repulsive forces between two identical charged conducting spheres - AQA - A-Level Physics - Question 4 - 2019 - Paper 2
Question 4
Figure 3 shows an arrangement used to investigate the repulsive forces between two identical charged conducting spheres. The spheres are suspended by non-conducting ... show full transcript
Worked Solution & Example Answer:Figure 3 shows an arrangement used to investigate the repulsive forces between two identical charged conducting spheres - AQA - A-Level Physics - Question 4 - 2019 - Paper 2
Step 1
Calculate the potential of one of the spheres.
Answer
The potential ( V ) of a sphere can be calculated using the formula:
where ( Q ) is the charge on each sphere (52 nC = ( 52 \times 10^{-9} , \text{C} )) and ( C ) is the capacitance of the sphere given by ( C = 4 \pi \epsilon_{0} r ).
The radius ( r ) is 20 mm = 0.020 m. Plugging in the values:
Thus,
Therefore, the potential of one of the spheres is approximately 23,000 V.
Step 2
Draw labelled arrows on Figure 3 to show the forces on sphere B.
Answer
Label the forces acting on sphere B as follows:
- An upward arrow to represent the tension in the thread.
- A downward arrow indicating the gravitational force acting on sphere B.
- A horizontal arrow to the left showing the electrostatic repulsive force due to sphere A.
Step 3
Suggest a solution to one problem involved in the measurement of d in Figure 3.
Answer
One problem in measuring the distance d accurately is the inability to observe the exact point at which the centers of the spheres are aligned. To address this, a ruler with a finer scale could be used to measure d, ensuring that it is positioned parallel to the line connecting the centers of the spheres.
Step 4
Show that the magnitude of the electrostatic force on each sphere is about 4 × 10⁻³ N.
Answer
Using Coulomb's law, the electrostatic force ( F ) between two charged spheres is given by:
where ( k \approx 8.99 \times 10^9 , \text{N m}^2/ ext{C}^2 ), ( Q_1 ) and ( Q_2 ) are the charges on the spheres (both 52 nC), and ( r ) is the distance between the centers of the spheres (d = 0.040 m).
Substituting the values:
Step 5
Discuss whether this measurement is consistent with the other data in this investigation.
Answer
The angle of 7° observed by the student can be analyzed in context with the equilibrium of forces acting on the spheres. If the calculated electrostatic force (4 × 10⁻³ N) is significantly greater than the gravitational force acting on the spheres, this will contribute to a larger angle at equilibrium. The consistent results would suggest the angle is reasonable provided that the gravitational force is minimal compared to the electrostatic force.
Step 6
Deduce with a calculation whether this statement is valid.
Answer
To assess the validity of the student’s statement regarding gravitational force, calculate the gravitational force:
Where:
- Mass ( m = 3.2 \times 10^{-3} , \text{kg} )
- Acceleration due to gravity ( g = 9.81 , \text{m/s}^2 )
Thus,
Comparing with the earlier computed electrostatic force ( F \approx 4 \times 10^{-3} , \text{N} ):
The gravitational force is approximately 0.0314 N, which is relatively small compared to the electrostatic force; hence, the statement made by the student is not valid as the gravitational force does affect the equilibrium state.