Freda asked in Science & MathematicsPhysics · 6 months ago

a) Find the net Coulomb force in vector form on charge q1, due to the presence of charges on q2 and q3.

I did my best to type the "square" but the "o" on the top left is q1 (-3.0*10^-6) and below it is q3 (3*10^-6). The "o" at the bottom right is -3.0*10^-6.

b) If charges q2 and q3 were nailed in place, find the strength of the acceleration of charge q1, which has a mass of 12 g (0.012 kg).

Also the original problem: https://i.postimg.cc/4NFfKvmY/20190622-171246.jpg

I know that the vectors need to be divided up to find what the hypotenuse would be. At first, I just plugged the values into Coulomb's formula: Fc = k |q1*q2| / r^2

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• 6 months ago

a)

The force on q1 due to q3 (r=10cm = 0.1m) is:

F13 = k.q1.q3/r² = 9*10^9 * (-3*10^-6) * (3*10^-6) / 0.1² = -8.1N

The minus sign means attraction. So q1 is being pulled towards q3 which is the minus y direction. There is no x component. This means F13 has:

x component = 0

y component = -8.1N

__________

The diagonal (d) of the square is given by Pythagoras: d² = 0.1² + 0.1² = 0.02

The force on q1 due to q2 (with r=d so r² = d² = 0.02) is:

F12 = k.q1.q1/r² = 9*10^9 * (-3*10^-6)*(-3*10^-6)/0.02 = 4.05N

This is positive meaning repulsion. So q1 is being push away (up/left) from q2 along the square’s diagonal: so the force has a positive y component and a negative x component.

x component = -4.05cos(45º) = -2.8N

y component = 4.05sin(45º) = 2.8N

__________

The resultant force on q1 is the vector sum F = F13 + F11:

total of x components = 0 + (-2.8) = -2.8N

total of y components = 8.1 + 2.8 = 10.9N

So in vector format: F = -2.8Nî + 10.9Nĵ (sometimes written <2.8N, 10.9N>).

Check my arithmetic of course.

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b)

Find the magnitude of F using |F|= √((-2.8)² + 10.9²).

(Though it's best to use unrounded values to minimise rounding errors.)

Then acceleration a = |F|/m (remembering to convert m from grams to kg).

A 'Best Answer' is always appreciated where appropriate

• Steve4Physics
Lv 7
6 months agoReport

If you wanted the value of d, then yes, it is √0.02 = 0.14142...
But there's no need to work out d in this problem.
F = kq1.q2/d². So it is ***the value of d²*** you Ineed (=0.02).