Questions: 3. Common static electricity involves charges ranging from nanocoulombs to microcoulombs. (a) How many electrons are needed to form a charge of -4.00 nC (b) How many electrons must be removed from a neutral object to leave a net charge of +0.2500 μC?

3. Common static electricity involves charges ranging from nanocoulombs to microcoulombs. (a) How many electrons are needed to form a charge of -4.00 nC (b) How many electrons must be removed from a neutral object to leave a net charge of +0.2500 μC?
Transcript text: 3. Common static electricity involves charges ranging from nanocoulombs to microcoulombs. (a) How many electrons are needed to form a charge of -4.00 nC (b) How many electrons must be removed from a neutral object to leave a net charge of $+0.2500 \mu \mathrm{C}$?
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Solution

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Solution Steps

Step 1: Determine the charge of a single electron
  • The charge of a single electron is e=1.602×1019 e = -1.602 \times 10^{-19} coulombs.
Step 2: Calculate the number of electrons for -4.00 nC
  • Given charge Q=4.00 Q = -4.00 nanocoulombs (nC).
  • Convert nanocoulombs to coulombs: Q=4.00×109 Q = -4.00 \times 10^{-9} coulombs.
  • Use the formula n=Qe n = \frac{Q}{e} to find the number of electrons.
  • n=4.00×1091.602×1019 n = \frac{-4.00 \times 10^{-9}}{-1.602 \times 10^{-19}} .
Step 3: Perform the calculation
  • n2.50×1010 n \approx 2.50 \times 10^{10} electrons.
Step 4: Calculate the number of electrons to be removed for +0.2500 μC
  • Given charge Q=+0.2500 Q = +0.2500 microcoulombs (μC).
  • Convert microcoulombs to coulombs: Q=0.2500×106 Q = 0.2500 \times 10^{-6} coulombs.
  • Use the formula n=Qe n = \frac{Q}{e} to find the number of electrons.
  • n=0.2500×1061.602×1019 n = \frac{0.2500 \times 10^{-6}}{1.602 \times 10^{-19}} .
Step 5: Perform the calculation
  • n1.56×1012 n \approx 1.56 \times 10^{12} electrons.

Final Answer

(a) 2.50×1010 \boxed{2.50 \times 10^{10}} electrons

(b) 1.56×1012 \boxed{1.56 \times 10^{12}} electrons

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