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Physics / Chapter 21: Electric Charge / Section 21-5

Charge Is Conserved — Question 8

Section 21-5 · Physics pages 3466–3467

Question 8 Conservation alone does not enforce uniform charge per unit mass An isolated insulating object of mass 100 g carries −10.0 nC and breaks into pieces A and B of masses 40 g and 60 g. No charge escapes. A model of perfectly uniform initial charge per unit mass predicts proportional fragment charges, but a measurement gives QA = −3.0 nC. 40 g 60 g Schematic; labels, not drawing lengths, specify the data. (a) Find the proportional-model prediction for both fragments and the charge of B required by the actual A measurement. (b) Compare the two actual charge-to-mass ratios. Determine whether the measurement rejects charge conservation, uniform partition, or both.
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Question 8 - Solution Conservation alone does not enforce uniform charge per unit mass 40 g 60 g (a) Method and calculation ( Q m ) uniform = −10.0/100 = −.100 nC/g. QA,uniform = −4.0 nC, QB,uniform = −6.0 nC. QB,actual = −10.0 −(−3.0) = −7.0 nC. (b) Interpretation and further calculation QA/mA = −.0750 nC/g, QB/mB = −.116667 nC/g. QA + QB = −3.0 −7.0 = −10.0 nC. The measured partition is consistent with conservation but inconsistent with a uniform proportional partition. Initial nonuniformity or redistribution during breakup could account for the difference. Physical check A conservation law fixes a total, not every spatial allocation of that total.

Question 8

Conservation alone does not enforce uniform charge per unit mass

An isolated insulating object of mass 100 g carries −10.0-10.0 nC and breaks into pieces A and B of masses 40 g and 60 g. No charge escapes. A model of perfectly uniform initial charge per unit mass predicts proportional fragment charges, but a measurement gives QA=−3.0Q_A=-3.0 nC.

Diagram shown in the original SVG worksheet.

  1. Find the proportional-model prediction for both fragments and the charge of B required by the actual A measurement.

  2. Compare the two actual charge-to-mass ratios. Determine whether the measurement rejects charge conservation, uniform partition, or both.

Question 8 - Solution

Conservation alone does not enforce uniform charge per unit mass

Diagram shown in the original SVG worksheet.

(a) Method and calculation

(Qm)uniform=−10.0/100=−.100nC/g.\left(\frac Qm\right)_{\mathrm{uniform}}=-10.0/100=-.100\,\mathrm{nC/g}.QA,uniform=−4.0nC,QB,uniform=−6.0nC.Q_{A,\mathrm{uniform}}=-4.0\,\mathrm{nC},\quad Q_{B,\mathrm{uniform}}=-6.0\,\mathrm{nC}.QB,actual=−10.0−(−3.0)=−7.0nC.Q_{B,\mathrm{actual}}=-10.0-(-3.0)=-7.0\,\mathrm{nC}.

(b) Interpretation and further calculation

QA/mA=−.0750nC/g,QB/mB=−.116667nC/g.Q_A/m_A=-.0750\,\mathrm{nC/g},\quad Q_B/m_B=-.116667\,\mathrm{nC/g}.QA+QB=−3.0−7.0=−10.0nC.Q_A+Q_B=-3.0-7.0=-10.0\,\mathrm{nC}.The measured partition is consistent with conservation but inconsistent with a uniform proportional partition. Initial nonuniformity or redistribution during breakup could account for the difference.

Physical check

A conservation law fixes a total, not every spatial allocation of that total.

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