Please show work and explain A source charge q_1 of unknown value is at an unkno

Question

Please show work and explain

A source charge q_1 of unknown value is at an unknown position on the y-axis. A test charge q_2 = -5.0 mu C, is located at the origin. The source charge causes an electrostatic force of 12.5 N in the positive y-direction to act on the test charge. Use k_e = 9.0 times 10^9 N middot m^2/C^2. a) At the origin, what is the magnitude and direction of the electric field E^rightvector_1 caused by the source charge? b) If the source charge is 10.0 cm away from the test charge, what is the magnitude of the source charge? c) If the source charge is negative, what are its coordinates? d) The test charge is replaced by another test charge of -5.0 mu C. Find the magnitude and direction of the electric force on this new test charge. Do not use Coulomb's Law: There is a much easier way to do this.

Explanation / Answer

a)

let the source charge is located at position above the origin along Y-axis

q1 = source charge

q2 = test charge = - 5 x 10-6 C

r = distance of source charge from origin

F = force on the test charge by the source charge = 12.5 N

using coloumb's law

F = k q1 q2 /r2

12.5 = (9 x 109) (5 x 10-6 ) (q1/r2)

q1/r2 = 0.000278 eq-1

electric field by the source charge at the origin is given as

E = k q1/r2 = (9 x 109) (0.000278) = 2.5 x 106 N/C

direction : negative Y-direction

b)

r = 10 cm = 0.1 m

using eq-1

q1/r2 = 0.000278

q1/(0.1)2 = 0.000278

q1 = 2.78 x 10-6 C

c)

(0 , - 10) cm

d)

since the magnitude of test charge remains same , hence the magnitude of force on the test charge remains 12.5 N

direction : positive Y-direction

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