Question 740: Electrostatics & Capacitance

Question

Suppose the charge of a proton and an electron differ slightly. One of them is $$-$$e, the other is (e + $$\Delta $$e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (musch greater than atomic size) apart is zero, then $$\Delta $$e is of the order of
[Given : mass of hydrogen m
h
= 1.67 $$ 	imes $$ 10$$-$$
27
kg]

Accepted Answer

According to question, the net electrostatic force (F
E
) = gravitational force  (F
G
)
F
E
= F
G
$$ \Rightarrow {1 \over {4\pi {\varepsilon _0}}}{{\Delta {e^2}} \over {{d^2}}} = {{G{m^2}} \over {{d^2}}}$$
$$ \Rightarrow \Delta e = m\sqrt {{G \over K}} \left( {{1 \over {4\pi {\varepsilon _0}}} = k = 9 	imes {{10}^9}} ight)$$
$$ = 1.67 	imes {10^{ - 27}}\sqrt {{{6.67 	imes {{10}^{ - 11}}} \over {9 	imes {{10}^9}}}} $$
$$\Delta e \approx 1.436 	imes {10^{ - 37}}C$$

Answer

10
$$-$$23
C

Answer

10
$$-$$37
C

Answer

10
$$-$$47
C

Answer

10
$$-$$20
C

Electrostatics & Capacitance

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