Two charges are located on a horizontal axis. Determine the electric field at p

Question

Two charges are located on a horizontal axis. Determine the electric field at p on a vertical axis as shown in the figure, where up is positive. The Coulomb constant is 8.98755 Times 109 N m2/C2. Answer in units of V/m Find the vertical component of the electric force on a -3.8 mu C charge placed at point p. Answer in units of N Two charges are located in the (x, y) plane as shown. The fields produced by these charges are observed at a point p with coordinates (0, 0). Find the x-component of the electric field at p. The value of the Coulomb constant is 8.98755 Times 109 N m2/C2. Answer in units of N/C In 1909 Robert Millikan was the first to find the charge of an electron in his now-famous oil drop experiment. In the experiment tiny oil drops are sprayed into a uniform electric field between a horizontal pair of oppositely charged plates. The drops are observed with a magnifying eyepiece, and the electric field is adjusted so that the upward force q E on some negatively charged oil drops is just sufficient to balance the downward force mg of gravity. Millikan accurately measured the charges on many oil drops and found the values to be whole-number multiples of 1.6 Times 10-19 C - the charge of the electron. For this he won the Nobel Prize. If a drop of mass 2.44898 Times 10-13 kg remains stationary in an electric field of 1 Times 106 N/C, what is the charge on this drop? The acceleration due to gravity is 9.8 m/s2 . Answer in units of C Three positive charges are arranged as shown at the corners of a rectangle. Find the magnitude of the electric field at the fourth corner of the rectangle. The value of the Coulomb constant is 8.98755 Times 109 N - m2/C2. Answer in units of N/C What is the direction of this electric field (as an angle measured from the positive x-axis, within limits of -180 degree to 180 degree, with counterclockwise positive)? Answer in units of degree What is the direction of this electric field (as an angle measured from the positive x-axis, within limits of -180 degree to 180 degree, with counterclockwise positive)? Answer in units of degree

Explanation / Answer

1) by symmetry only y component

Ey = 2 E sin theta = 2*9.0E9*2.7E-6/(3^2 + 1.5^2) * 1.5/sqrt(3^2 + 1.5^2)= 1932 V/m

2) Fy = q Ey = -3.8E-6*1932=-7.34E-3 N

3) sum x components

Ex = 9.0E9*8.8/(2.1^2 +1.6^2)*2.1/sqrt(2.1^2 + 1.6^2)-9.0E9*9/(2.1^2 +1.5^2)*2.1/sqrt(2.1^2 + 1.5^2)

Ex = -8.58E8 N/C

5) if stationary
qE - mg = 0

q = mg/E = 2.44898E-13*9.81/1.0E6=2.40E-18 C

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