Question

1.)Three point charges are located in the xy-plane; -2.0nC at (1,1), +5.0 nC at (0,2) abd 1.0 nC at (2,3) calculate the magnitude of the electric field at the origin.

2.) For the above problem, determine the magnitude (only) of the accleration of a proton placed at the origin.

Answer 1

Electric Field of Point Charge

The electric field of a point charge can be obtained from Coulomb's Law:

The electric field from any number of point charges can be obtained from a vector sum of the individual fields. A positive number is taken to be an outward field; the field of a negative charge is toward it.

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1

In the given problem, we will calculate the electric fields due to individual charges and then add them up to get the net electric field at the origin :

Field due to -2.0 nC =

= (9cos45 i + 9sin45 j )

Field due to +5.0nC =

= -11.25 j

Field due to +1.0 nC =

= -0.384 i - 0.576 j

Thus, net field is :

Thus , magnitude of net electric field is :

2.Magnitude of acceleration :

Charge on a proton = 1.6 x 10^-19 C

Thus, force on the proton is :

Thus, acceleration =