A \(-50 \mathrm{nC}\) charged particle is in a uniform electric field \(\mathbb{N}\). \(\vec{E}=(10 \mathrm{~V} / \mathrm{m}\), east \()\). An external force moves the particle \(1.0 \mathrm{~m}\) north, then \(5.0 \mathrm{~m}\) east, then \(2.0 \mathrm{~m}\) south, and finally \(3.0 \mathrm{~m}\) west. The particle begins and ends its motion with zero velocity.

a. How much work is done on it by the external force?

b. What is the potential difference between the particle's final and initial positions?