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3:09 × Drill Set 1-new-PHYS 242.docx 2. (i A uniformly charged ring has radius a-0.15m and total charge Q- 24 nC (see figure below) 0 What is the circumference of the ring, and thus the charge per unit length (charge density) of the ring Cm) charge density (ii) To find the potential (voltage) at point (P) distant (along the rings axis) from the ring center, we can first find the E-field as we did in chapter 21, by considering the contributions to the E-field from an clemental charge on the ring. Symmetry then showed that only the component of the E- field that points in the direction of the axis of the ring (at points on the axis) survives. Hence it is easy to perform the integral O going along the ring axis from to x, to get V(). Alternatively, we already know the petential everywhere of a point charge. So for an clemental charge dq, the contribution to the potential at pont P is: (where) charges in the ring, and obtain an expression for the potential (voltage) V at x (on the ring axis) (Hint: where ρ is charge density, ds is elemental length; Also, , a, r, de not vary as we perform the integration over the charges on the ring. Also, k-9x 10 (SI units)) 5 Open With Print
3:09 XDrill Set 1 -new - PHYS 242.docx potential (voltage) V at x (on the ring axis) (Hint: where ρ is charge density, ds is elemental length; Also, x, a, r, do not vary as we perform the integration over the charges on the ring Also, k-9 x 10 (SI units)) V(x) (ii) What is the voltage (the potential energy of+1C)atx 0.3 m, and at the center of the ring. Voltage (at x-0.3m) Voltage at center of ring = (iv) What is the potential energy of a small ball (treatod as a point charge) of mass 0.0015 kg and charge-3 x 10, C, located at x-0.3 m. If the location of the ball is changed to the center of the ring, what is the new potential energy Potential energy (at x-0.3 m)- Potential energy at center of ring (J)% (v) If the small ball is released from rest at x-0.3 m what is the speed of the ball at the center of the ring. assuming the ball is constrained to move only along the axis of the ring. (Hint: employ the mechanical energy conservation law: Velocity (m/s) 5 Open With Print
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