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1. What is the strength of the electric field at the position indicated by the dot in the figure?

2. What is the direction of the electric field at the position indicated by the dot in the figure? Specify the direction as an angle above the horizontal line.

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1 Answer

  • Electric field E1 due to charge at the top in the horizontal direction

    = kq/r^2

    = 9 x 10^9 x 1 x 10^-9 / (0.05)^2 N/C

    = 3600 N/C.

    Electric field E2 due to the lower charge making an angle θ with the horizontal

    = 9 x 10^9 x 1 x 10^-9 / [(0.05)^2 + (0.10)^2]

    = 720 N/C

    Horizontal component of E2

    = E2 cosθ

    = 720 * 5/√[5^2 + 10^2]

    = 322 N/C

    Vertical component of E2

    = E2 sinθ

    = 720 * 10/√[5^2 + 10^2]

    = 644 N/C

    Total horizontal component of net electric field, E

    = 3600 + 322 = 3922 N/C

    Total vertical component of E

    = 644 N/C

    Resultant E

    = √[(3922)^2 + (644)^2]

    = 3974.5 N/C

    If it makes an angle α with the horizontal,

    tanα = 644/3922

    => α = 9.32°.

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