Two negative charges, each with a charge of -7.7 nC, are at fixed locations as shown below. A proton is launched from the midpoint of the line joining the charges in a direction perpendicular to the line joining the charges. Find the minimum initial velocity of the proton that will allow it to escape to infinity. Ignore gravitational or any other influences on the proton. (k=1/480 = 8.99 × 109 Nm2/C2, e = 1.60 × 10-19 C, mproton = 1.67 × 10-27 kg). [Hint: Conservation of energy might be helpful and you can assume that the proton is at rest at infinity]

A constant electric field of 20.0 N/C points along the positive x-direction. An electron, initially at rest, moves a distance of 0.500 m in this space. How fast is the electron moving after its 0.500 m journey?

Two point charges each with 0.15 CC of charge are 5.0×10−2 mm apart. Knowing that k is 9×10^9N⋅m^2/C  (the proportionality constant for Coulomb's law), find the force between the charges. Express your answer to two significant figures and include the appropriate units.

A 1.86  10-9 C charge has coordinates x = 0, y = −2.00; a 3.21  10-9 C charge has coordinates x = 3.00, y = 0; and a -5.20  10-9 C charge has coordinates x = 3.00, y = 4.00, where all distances are in cm. Determine magnitude and direction for the electric field at the origin and the instantaneous acceleration of a proton placed at the origin. (a) Determine the magnitude and direction for the electric field at the origin (measure the angle counterclockwise from the positive x-axis). magnitude   direction  ° (b) Determine the magnitude and direction for the instantaneous acceleration of a proton placed at the origin (measure the angle counterclockwise from the positive x-axis). magnitude   direction  °

Two identical point charges (q= +2.20 x 106 C) are fixed at opposite corners of a square whose sides have a length of 0.450 m. A test charge (qo = -3.10 x 108 C), with a mass of 9.40 x 10-8 kg, is released from rest at one of the corners of the square. Determine the speed of the test charge when it reaches the center of the square. Number i Units VR ·90

Charge q1 = 1.50 nC is at x1 = 0 and charge q2 = 5.00 nC is at x2 = 4.00 m. At what point between the two charges is the electric field equal to zero? (Enter the x coordinate in m.)

An electron is moving east in a uniform electric field of 1.50 N/C directed to the west. At point A, the velocity of the electron is 4.55×105 m/s pointed toward the east. What is the speed of the electron when it reaches point B, which is a distance of 0.400 m east of point A?

An infinitely long line of charge has linear charge density 5 x 10-12 C/m. A proton is at distance 13 cm from the line and moving directly toward the line at speed 0.5 × 103 m/s. How close (in cm) does the proton get to the line of charge?