Consider an electron in front of metallic surface of a distance d. Assume the force of attraction by the plate is given as <math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>4</mn></mrow></mrow></mfrac><mfrac><mrow><mrow><msup><mrow><mrow><mi mathvariant="bold-italic">q</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>4</mn><mi mathvariant="bold-italic">π</mi><msub><mrow><mrow><mi mathvariant="bold-italic">ε</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub><msup><mrow><mrow><mi mathvariant="bold-italic">d</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></mrow></mrow></mfrac></math> . Calculate work in taking the to an infinite distance from the plate .Taking d=0.1 nm. find the work done in electron volts?

Explanation- Fx= 14q24? ? 0x2W= ? d? fdx = ? d? q2dx4*4? ? 01x2= q24*4? ? 01d= (1.6*10-19)2*9*1094*10-10 J= 3.6eV

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Consider an electron in front of metallic surface of a distance d. Assume the force of attraction by the plate is given as $\frac{1}{4} \frac{q^{2}}{4 π ε_{0} d^{2}}$ . Calculate work in taking the to an infinite distance from the plate .Taking d=0.1 nm. find the work done in electron volts?

1 View | Posted 3 months ago

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Pallavi Pathak | Contributor-Level 10

3 months ago

Explanation- F_x= $\frac{1}{4} \frac{q^{2}}{4 ? ?_{0} x^{2}}$

W= $?_{d}^{?} f d x$ = $?_{d}^{?} \frac{q^{2} d x}{4 * 4 ? ?_{0}} \frac{1}{x^{2}}$

= $\frac{q^{2}}{4 * 4 ? ?_{0}} \frac{1}{d}$

= $\frac{{(1.6 * 10^{- 19})}^{2} * 9 * 10^{9}}{4 * 10^{- 10}}$ J= 3.6eV

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