Physics

Problem

Two identical positive point charges, each of charge

+5.0\,\mu\text{C}

, are fixed in space on the

x

–axis at

x=-0.20\,\text{m}

and

x=+0.20\,\text{m}

. A point

P

is located on the positive

y

–axis at

y=0.30\,\text{m}

. Assume vacuum conditions and neglect all other influences. (a) Identify the direction of the net electric field at point

P

relative to the coordinate axes. (b) Describe qualitatively how the vector contributions from the two charges combine to give the direction you stated in part (a). In your explanation, refer explicitly to symmetry and to the components of the individual field vectors. (c) The charges are simultaneously doubled to

+10.0\,\mu\text{C}

each while their positions remain unchanged. Explain whether the direction and the magnitude of the net electric field at

P

change, and justify your answer.

Intuitive explanation

The key is recognizing that both charges push outward on a test charge at $P$ , so you must add the electric field vectors from each charge—not just their magnitudes. By symmetry, the horizontal components cancel, leaving only the vertical component. Use Coulomb's law to find each field's magnitude, then geometry (the distance from each charge to $P$ ) to find how much of that field points upward.

Intuitive explanation

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