Two bodies X and Y carry charges -6.6 microcolumb and -5 microcolumb. How many electron should be transferred from X to Y so they acquire equal charge

Two bodies X and Y carry charges −6.6×10

−6
C and −5×10
−6
C respectively.
⇒ X has excess charge of −1.6×10
−6
C composed to Y.
⇒ X has to give a charge −0.8×10
−6
C if charge on both have to be same.
The charge on one electron is −1.6×10
−19
C
⇒ Number of electrons required to transfer a charge of −0.8×10
−6
C
=
−1.6×10
−19

−0.8×10
−6


=5×10
12

To find out how many electrons need to be transferred from body X to body Y in order for them to acquire equal charge, we need to convert the given charges from microcoulombs to the charge of an electron.

The charge of an electron is approximately 1.602 x 10^-19 coulombs.

Let's calculate the charge of body X in terms of electrons:

Charge of body X = -6.6 microcoulombs * (1 coulomb / 10^6 microcoulombs) * (1 electron / 1.602 x 10^-19 coulombs) = -4.116 x 10^13 electrons

Similarly, let's calculate the charge of body Y in terms of electrons:

Charge of body Y = -5 microcoulombs * (1 coulomb / 10^6 microcoulombs) * (1 electron / 1.602 x 10^-19 coulombs) = -3.119 x 10^13 electrons

To make the charges equal, we need to transfer electrons from body X to body Y. The difference in the number of electrons between them is:

Difference in charge = |Charge of body X| - |Charge of body Y| = (-4.116 x 10^13 electrons) - (-3.119 x 10^13 electrons) = -0.997 x 10^13 electrons

Since the charges of X and Y are negative, transferring electrons from body X to body Y will reduce the charge on body X and increase the charge on body Y, eventually making them equal. Therefore, we need to transfer approximately 0.997 x 10^13 electrons from body X to body Y.

To find out how many electrons should be transferred from body X to body Y so that they acquire equal charge, we need to know the charge of a single electron.

The charge of a single electron is approximately -1.6 x 10^-19 coulombs.

To calculate the number of electrons required, we can use the formula:

Number of electrons = Total charge / Charge of a single electron

The total charge is the difference between the charges of bodies X and Y.

Total charge = Charge of body Y - Charge of body X

Plugging in the given values:

Total charge = (-5 x 10^-6 C) - (-6.6 x 10^-6 C)

Total charge = 1.6 x 10^-6 C

Now, let's calculate the number of electrons:

Number of electrons = (1.6 x 10^-6 C) / (-1.6 x 10^-19 C)

Number of electrons ≈ -1 x 10^13 electrons (approximation)

Since the charge of an electron is negative, we don't need to take the absolute value of the number of electrons.

Therefore, approximately 1 x 10^13 electrons should be transferred from body X to body Y so that they acquire equal charge.

The difference between -5 mC and -6.6 mC is 1.6 mC. Half of this amount, 0.8 mC, is how much charge the -6.6 mC body must give to the other body so that they are equally charged.

0.8 mC x 6.24150975⋅10^15e/mC
= _______ electrons