Explain why the work needed to move a particle with charge Q through a potential difference ΔV is W = Q ΔV. whereas the energy stored in a charged capacitor is U_E = QΔV Where does the factor come from?

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Supratim PalLv10

6 Mar 2021

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Two parallel plates are charged with +Q and -Q respectively as shown in the figure, where Q = 26 nC. The area of each plate is A = 0.019 m2 The distance between them is d = 6.4. cm. The plates are in the air.

Part a. With the information given, write the equation of the capacitance in terms of ε0, A, d.

Part b. Solve for the numerical value of C in pF

Part c. With the information given, express the potential difference across the capacitor in terms of Q and C.

Part d. Solve for the numerical value of ΔV in V.

Part e. If the charges on the plates are increased to 2Q, what is the value of the capacitance C in pF?

Part f. If A is then increased to 2A, d is decreased to d/4, what is the value of the capacitance C in pF?

Part g. What is the new value of potential difference ΔV in V with the original charge Q, given the values for A and d from part (f)?

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A proton (charge +e, mass m_p), a deuteron (charge +e, mass 2m_p), and an alpha particle (charge +2e, mass 4m_p) are accelerated from rest through a common potential difference ΔV. Each of the particles enters a uniform magnetic field , with its velocity in a direction perpendicular to . The proton moves in a circular path of radius r_p. In terms of radius r_p, determine the radius r_dof the circular orbit for the deuteron.