A point charge of q = 4 mu C is located at r = (4 I^hat, jcirc)cm. Another point

Question

A point charge of q = 4 mu C is located at r = (4 I^hat, jcirc)cm. Another point charge of Q = -7 mu C is located at R = (6 i^hat + 4 jcirc)cm. k_e = 9 times 10^0 Nm^2/C^3 = 90 N cm^2/mu C^4 Calculate the potential energy of the system (Be careful of units) Calculate the x-component of the force on q. Calculate the y-component of the force on Q Use Gauss's law to calculate the electric field due to infinite plate of charge If the areal charge density is sigma = 5 mu C/cm^2, what is the force vector on an electron (q = - epsilon = 1 1.60 times 10^-23 mu C) ten centimeters above the plane?

Explanation / Answer

Given

point charges q = 4*10^-6 C, at (x1,y1)=(4,2) ;.

Q = -7*10^-6 C at (x2,y2) = (6,4).

a.
the potential energy of the system is U = kq1q2/r

here the distance between the point charges is r = sqrt((y2-y1)^2+(x2-x1)^2)

           r = sqrt((4-2)^2+(6-4)^2) cm = 2.83 cm = 0.0283 m

now U = 9*10^9(4*10^-6)(-7*10^-6)/(0.0283) J

   = -8.905 J

b.

the force between the charges is F = kq1*q2/r^2

               F = 9*10^9*(4*10^-6)(7*10^-6)/(0.0283)^2 N

               F = 314.65 N

Fx = F cos 45 = 314.65 cos 45 = 222.5 N

the direction of force on Q is in the third quadrant 45 degrees from the x axis it is 225 degrees

so the y component of force on Q is Fy = F sin 225 = 314.65 sin225 = -222.49 N in the -ve y direction

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