Net force on a particle. Consider the following two \"fixed\" charges with locat

Question

Net force on a particle. Consider the following two "fixed" charges with locations on a plain given by x and y.

Particle a: -1.00cm, 2.00cm, charge of -5.0 uC

Particle b: 3.00cm, -1.00cm, charge of +3.0 uC

1) Find the magnitude of the force on b from a, and then give the force in component form (i.e. x-component and y- component)?

2) Now assume this region has an additional uniform electric field (from some external source), with a magnitude of (1.5x10^7 V/m) directed (60 degrees above from the x axis). Find the force on particle b from this externa field and give it in component form?

3) Combine the two forces on b (from particle a and external field) via vector addition. Give the net force in component form?

4) Give net force in magnitude-direction form?

5) Sketch of problem showing individual force and net force vector?

Explanation / Answer

direction of force will be along ba.

ba = a - b = (-0.01i + 0.02j) - (0.03i - 0.01j) = -0.04i + 0.03j m

|ba| = sqrt(0.04^2 + 0.03^2) = 0.05 m

F = k(qa)(qb) (ba) / (|ba|)^3

= (9 x 10^9 x 5 x 10^-6 x 3 x 10^-6 ) (-0.04i + 0.03j ) / 0.05^3

= - 43.2i + 32.4 j N

magnitude = sqrt(43.2^2 + 32.4^2) = 54 N

2) F' = qE = 3 x 10^-6 x 1.5 x 10^7 ( cos60i + sin60j)

F' = 22.5i + 38.97j N

3) Fnet = F + F' = - 20.7i + 71.37j N

4) magnitude = sqrt(20.7^2 + 71.37^2) = 74.31 N

angle = 180 - tan^-1(71.37/20.7) = 106.17 deg

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