To determine the kinetic energy of the charge at point [tex]\( B \)[/tex], we can use the principle of conservation of energy. The total mechanical energy (sum of potential energy and kinetic energy) remains constant when only conservative forces (like electric forces) are involved.
Given the data:
- Potential energy at point [tex]\( A \)[/tex] [tex]\((U_A)\)[/tex] = [tex]\( 5.6 \times 10^{-10} \)[/tex] joules
- Potential energy at point [tex]\( B \)[/tex] [tex]\((U_B)\)[/tex] = [tex]\( 2.3 \times 10^{-10} \)[/tex] joules
- Kinetic energy at point [tex]\( A \)[/tex] [tex]\((K_A)\)[/tex] = 0 joules
According to the conservation of energy:
[tex]\[ \text{Total energy at point A} = \text{Total energy at point B} \][/tex]
At point [tex]\( A \)[/tex]:
[tex]\[ U_A + K_A = 5.6 \times 10^{-10} \text{ joules} + 0 \text{ joules} = 5.6 \times 10^{-10} \text{ joules} \][/tex]
At point [tex]\( B \)[/tex]:
[tex]\[ \text{Total energy at point B} = U_B + K_B \][/tex]
Since the total energy is conserved:
[tex]\[ \text{Total energy at point A} = \text{Total energy at point B} \][/tex]
This gives us:
[tex]\[ 5.6 \times 10^{-10} \text{ joules} = 2.3 \times 10^{-10} \text{ joules} + K_B \][/tex]
Solving for [tex]\( K_B \)[/tex]:
[tex]\[ K_B = 5.6 \times 10^{-10} \text{ joules} - 2.3 \times 10^{-10} \text{ joules} \][/tex]
[tex]\[ K_B = 3.3 \times 10^{-10} \text{ joules} \][/tex]
Hence, the kinetic energy at point [tex]\( B \)[/tex] is [tex]\(\boxed{3.3 \times 10^{-10} \text{ joules}}\)[/tex].
The correct answer is:
D. [tex]\(3.3 \times 10^{-10} \text{ joules}\)[/tex]
