Step-by-step explanation:
To find the work required to move the test charge from a point midway between the charges to a point 1.1 cm closer to one of the charges, we need to calculate the change in potential energy of the test charge.
The potential energy between two charges can be calculated using the equation:
U = k*q1*q2/r
where U is the potential energy, k is Coulomb's constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
The work done to move the test charge against the electric field is equal to the change in potential energy of the test charge:
Work = ΔU = U_final - U_initial
Let's calculate the initial and final potential energies of the test charge.
Initial potential energy:
To calculate the initial potential energy, we need to find the distance between the test charge and each of the point charges when the test charge is midway between them. Since the charges are identical, the distances from the test charge to each point charge are equal.
Distance initial = (6.5 cm + 1.1 cm/2) = 6.5 cm + 0.55 cm = 7.05 cm = 0.0705 m
Using the equation for potential energy, the initial potential energy is:
U_initial = k*q_test*q_charge/r_initial
U_initial = (9 x 10^9 Nm^2/C^2)*(0.16 x 10^-6 C)*(21 x 10^-6 C)/(0.0705 m) = 8.94 J
Final potential energy:
To calculate the final potential energy, we need to find the new distance between the test charge and one of the point charges when the test charge is moved 1.1 cm closer.
Distance final = (6.5 cm - 1.1 cm) = 5.4 cm = 0.054 m
Using the equation for potential energy, the final potential energy is:
U_final = k*q_test*q_charge/r_final
U_final = (9 x 10^9 Nm^2/C^2)*(0.16 x 10^-6 C)*(21 x 10^-6 C)/(0.054 m) = 11.9 J
The work required to move the test charge from the initial point to the final point is:
Work = ΔU = U_final - U_initial
Work = 11.9 J - 8.94 J = 2.96 J
Therefore, the work required by an external force to move the test charge is approximately 2.96 J.