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anonymous

  • one year ago

Two small insulating spheres with radius 5.00×10−2 m are separated by a large center-to-center distance of 0.600 m . One sphere is negatively charged, with net charge -2.10 μC , and the other sphere is positively charged, with net charge 3.70 μC . The charge is uniformly distributed within the volume of each sphere. What is the magnitude E of the electric field midway between the spheres? Take the permittivity of free space to be ϵ0 = 8.85×10−12 C2/(N⋅m2) .

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  1. Michele_Laino
    • one year ago
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    hint: here is the situation of your problem: |dw:1436365695363:dw|

  2. Michele_Laino
    • one year ago
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    where \[\begin{gathered} {Q_1} = 3.70 \times {10^{ - 6}}coulombs \hfill \\ {Q_2} = - 2.10 \times {10^{ - 6}}coulombs \hfill \\ \end{gathered} \]

  3. Michele_Laino
    • one year ago
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    now the total electric field at midpoint M, is given by the subsequent vector sum: \[\large {\mathbf{E}}\left( M \right) = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_1}}}{{{{\left( {d/2} \right)}^2}}}{\mathbf{\hat x}} + \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_2}}}{{{{\left( {d/2} \right)}^2}}}{\mathbf{\hat x}}\] |dw:1436367402248:dw|

  4. Michele_Laino
    • one year ago
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    oops.. the total electric field at midpoint M is: \[\large {\mathbf{E}}\left( M \right) = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_1}}}{{{{\left( {d/2} \right)}^2}}}{\mathbf{\hat x}} - \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_2}}}{{{{\left( {d/2} \right)}^2}}}{\mathbf{\hat x}}\]

  5. Michele_Laino
    • one year ago
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    and the requested magnitude is: \[\large E\left( M \right) = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_1}}}{{{{\left( {d/2} \right)}^2}}} - \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_2}}}{{{{\left( {d/2} \right)}^2}}}\]

  6. Michele_Laino
    • one year ago
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    where you have to substitute these quantities: \[\Large \begin{gathered} {Q_1} = 3.70 \times {10^{ - 6}} \hfill \\ {Q_2} = - 2.10 \times {10^{ - 6}} \hfill \\ \end{gathered} \]

  7. anonymous
    • one year ago
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    Yes, it's usually safer to compute each E before adding them. the r = d/2 happens to be the situation here ... it does NOT mean "radius = diameter/2 " <= NO!

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