A thin ring of radius R carries a uniform charge Q (assumed positive) as shown. 11. Find an expression for the electrostatic potential along the z-axis, V(z). 12. Now find the electric field along the z-axis and show that you get correct results when you set z=0 and when z is large (but not infinite). P 13. Now assume a positive point charge Q starts at rest from the center of the ring and is given a slight nudge in the z direction. Find an expression for its speed when it is far from the ring. 14. Instead of a charged ring, consider current I flowing clockwise from the point of Họi dĩ x ê 4n r2 view of P. Using the Biot-Savart Law, dB : find the magnetic field along the z-axis.

A thin ring of radius R carries a uniform charge Q (assumed positive) as shown. 11. Find an expression for the electrostatic potential along the z-axis, V(z). 12. Now find the electric field along the z-axis and show that you get correct results when you set z=0 and when z is large (but not infinite). P 13. Now assume a positive point charge Q starts at rest from the center of the ring and is given a slight nudge in the z direction. Find an expression for its speed when it is far from the ring. 14. Instead of a charged ring, consider current I flowing clockwise from the point of Họi dĩ x ê 4n r2 view of P. Using the Biot-Savart Law, dB : find the magnetic field along the z-axis.