A + 6 mu C test charge with a mass of 50 g is held in place 20 cm from a -8 mu C

Question

A + 6 mu C test charge with a mass of 50 g is held in place 20 cm from a -8 mu C source charge. a. What is the magnitude of the electric force on the positive test charge? b. What is the magnitude of the electric field at the positive test charge's location? c. Calculate the electric potential at the positive test charge's location. d. How much work does it take to move the test charge infinitely far away from the source charge? Does this work translate into a gain or loss of kinetic energy? e. If you let the positive test charge go, it will move towards the source charge. Calculate the kinetic energy and velocity of the test charge before it hits the source charge.

Explanation / Answer

here,

test charge , q1 = + 6 * 10^-6 C

q2 = - 8 * 10^-6 C

m1 = 0.05 kg

x = 0.2 m

a)

the magnitude of the electric force , F = k * q1 * q2 /x^2

F = 9 * 10^9 * 6 * 10^-6 * 8 * 10^-6 /0.2^2 N

F = 10.8 N

b)

the magnitude of the electric feild , E = k * q2 /x^2

E = 9 * 10^9 * 8 * 10^-6 /0.2^2 N/C

E = 1.8 * 10^6 N/C

c)

the electric potential , V = k * q/x

V = 9 * 10^9 * (-8 * 10^-6) /0.2 V

V = - 3.6 * 10^5 V

d)

work done , W = V * q1

W = 2.16 J

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