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If ${10^{18}}$ electrons are taken out every second from a body, then how much time is required to get a total charge of $0.1C$ from it?
(A) $0.625s$
(B) $6.25s$
(C) $62.5s$
(D) $625s$

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Last updated date: 14th Jun 2024
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Answer
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Hint To solve this question, we need to compute the current flowing through the body by using its basic formula. For this we have to calculate the charge flowing through the body per second from the value of the number of electrons given. Finally, using the values of the current thus obtained, and the value of the charge given, we can get the value of the time required.
The formula which is used in solving this question is given by
$\Rightarrow I = \dfrac{{dq}}{{dt}}$, here $I$ is the current, $q$ is the charge, and $t$ is the time.

Complete step by step answer
We know that the current through a conductor is defined as the rate of flow of charge through it. Mathematically, it can be expressed as
$\Rightarrow I = \dfrac{{dq}}{{dt}}$ (1)
Now, we know that the total charge contained by a given number of electrons is given by
$\Rightarrow q = ne$
According to the question, we have $n = {10^{18}}$. Also we know that $e = 1.6 \times {10^{ - 19}}C$. Substituting these above we get
$\Rightarrow q = {10^{18}} \times 1.6 \times {10^{ - 19}}$
On solving, we get
$\Rightarrow q = 0.16C$
According to the question, this much amount of charge is taken out every second from the body. So we have
$\Rightarrow dq = 0.16C$, and
$\Rightarrow dt = 1s$
Substituting these in (1) we get
$\Rightarrow I = \dfrac{{0.16}}{1}$
$\Rightarrow I = 0.16A$ (2)
Now, from (1) we have
$\Rightarrow I = \dfrac{{dq}}{{dt}}$
Multiplying both sides by $dt$ we have
$\Rightarrow Idt = dq$
From (2)
$\Rightarrow 0.16dt = dq$
Integrating both sides, we get
$\Rightarrow 0.16\int\limits_0^T {dt} = \int\limits_0^Q {dq} $
$\Rightarrow 0.16\left[ t \right]_0^T = \left[ q \right]_0^Q$
On substituting the limits we get
$\Rightarrow 0.16T = Q$
$\Rightarrow T = \dfrac{Q}{{0.16}}$
According to the question, we have $Q = 0.1C$. So we get
$\Rightarrow T = \dfrac{{0.1}}{{0.16}}$
$\Rightarrow T = 0.625s$
Thus, the time required to get a total charge of $0.1C$ from the body is equal to $0.625s$.
Hence, the correct answer is option A.

Note
Instead of calculating the current, we could have used the unitary method to solve this question also. As we are given the amount of charge flowing in one second, so we can calculate the time required to get the given amount of charge by the unitary method.