In this problem, consider electrostatic forces only. In the figure, there is a p

Question

In this problem, consider electrostatic forces only. In the figure, there is a particle of charge +Q at x = 0, and there is a particle of charge +16Q at x = +4a. You are going to bring in a third particle, with a charge of 4Q, and place it at an appropriate spot on the x-axis.

Use Q = 60.0 106C, and a = 40.0 cm. Also, use k = 9.00 109 N · m2/C2.

(a)First, place the particle of charge 4Q at the correct location so that the +Q charge experiences no net force because of the other two charged particles. In that situation, calculate the magnitude of the force that just one of the other charged particles exerts on the +Q charge.

(b)Instead, at what location on the x-axis would you place the particle of charge 4Q so that the +16Q charge experiences no net force because of the other two charged particles? Note that we're looking for an answer in units of centimeters.

(c)Finally, place the particle of charge 4Q at the correct location so that the 4Q charge experiences no net force because of the other two charged particles. In that situation, calculate the magnitude of the force that just one of the other charged particles exerts on the 4Q charge.

Explanation / Answer

net force = electric field * charge

force will be 0 if net electric field is 0 on location

electric field = k * q / r^2

let at position x if -4Q charge is placed net force on Q change is 0 so,

net electric field at Q = k * -4Q / x^2 + k * 16Q / (4a)^2

k * -4Q / x^2 + k * 16Q / (4a)^2 = 0

-4 / x^2 + 16 / (4a)^2 = 0

-4 / x^2 + 16 / (4 * 0.4)^2 = 0

x = 0.8 m

a) -4Q charge should be placed at 0.8 m or 80 cm

magnitude of force = k * q1 * q2 / r^2

magnitude of force = 9 * 10^9 * 60 * 10^-6 * 4 * 60 * 10^-6 / (0.8)^2

a) magnitude of force = 202.5 N

for 16Q charge to experience no force let -4Q charge is placed at position x

so,

net electric field at 16Q = k * -4Q / x^2 + k * Q / (4a)^2

k * -4Q / x^2 + k * Q / (4a)^2 = 0

-4 / x^2 + 1 / (4a)^2 = 0

-4 / x^2 + 1 / (4 * 0.4)^2 = 0

x = 3.2 m

distance from origin = 3.2 - 4a

distance from origin = 3.2 - 1.4

distance from origin = 1.8 m

b) -4Q charge should be placed at -1.8 m or -180 cm

let at position x net electric field due to Q and 16 Q is 0 so

k * Q / x^2 - k * 16Q / (4a - x)^2 = 0

1 / x^2 - 16 / (4 * 0.4 - x)^2 = 0

x = 0.32 m

c) -4Q charge should be placed at 0.32 m or 32 cm

magnitude of force = 9 * 10^9 * 60 * 10^-6 * 4 * 60 * 10^-6 / (0.32)^2

c) magnitude of force = 1265.625 N

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