A particle with charge q on the negative x axis and a second particle with charge 2q on the positive x axis are each a distance d from the origin. Where should a third particle with charge 3q be placed so that the magnitude of the electric field at the origin is zero?

aA plastic rod of length = 24.0 cm is uniformly charged with a total charge of +12.0 C. The rod is formed into a semicircle with its center at the origin of the xy plane (Fig. P24.34). What are the magnitude and direction of the electric field at the origin? Figure P24.34

Is it possible for a conducting sphere of radius 0.10 m to hold a charge of 4.0 C in air? The minimum field required to break down air and turn it into a conductor is 3.0 106 N/C.

A uniform charge distribution of total charge Q (Q>0) is located along the x-axis. The left end of the charge distribution is located at x=-(144/13)m and its right end is located at x=(25/13)m. Our goal is to calculate the electric field at point P which is located at (x,y)=(0,d). Use letters k for the Coulomb constant, Q for the total charge, d for the y-coordinate of point P, and x and y, for the cartesian coordinates in your responses. (a) Determine the expression for dq. (b) Determine the expression for r2, the magnitude of the vector that is directed from the element of charge dq to the location in which the field is to be determined. (c) Determine the expression for r̂ the unit vector that is directed from the element of charge dq to the location in which the field is to be determined (d) Write the expression for d due to the element of charge dq. (e) Let d=(60/13)m. Integrate the expression to determine the electric field at P. Perform this integration by hand. Avoid using…

(a) Figure (a) shows a nonconducting rod of length L = 5.80 cm and uniform linear charge density λ = +4.87 pC/m. Take V = 0 at infinity. What is Vat point P at distance d= 7.50 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 4.87 pC/m. With V=0 at infinity, what is Vat P? L/2 (a) -L/2 L/21/2- (b)

A semi-infinite rod lies along the positive x-axis with its end at the origin. The rod carries a uniform linear charge density of λ = 1.5 μC/m. Point P is located on the positive y-axis a distance a = 0.45 m from the origin. Refer to the figure. Calculate the value of the x-component of the electric field at point P, in kilonewtons per coulomb, due to the semi-infinite charged rod.

Suppose a quarter circular-loop of thin wire with radius 0.50 m carries a line charge of A = 1.0 × 10-⁹. Calculate the electric field due to the electrostatic (uniform) line charge at the point P. Hint: Look at first PS file and video in module 9-10. Note: Anco = 9.0 × 10⁹

(a) Figure (a) shows a nonconducting rod of length L = 5.40 cm and uniform linear charge density λ = +4.41 pC/m. Take V = 0 at infinity. What is V at point P at distance d = 9.30 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 4.41 pC/m. With V= 0 at infinity, what is V at P? (a) Number i (b) Number i P ‡ ‡ ‡ ‡ + + + +‡‡ ‡ ‡‡ L/2 L/2 Units Units [+ + + ++++G ·L/2 L/2-

(a) Figure (a) shows a nonconducting rod of length L = 9.00 cm and uniform linear charge density λ = +7.57 pC/m. Take V = 0 at infinity. What is V at point P at distance d = 5.20 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 7.57 pC/m. With V = 0 at infinity, what is V at P? (a) Number i (b) Number i ·+· -L/2 (a) Units Units L/2 +‡ ‡ ‡+3= L/2 .Р (b) L/2