Question

An object has a charge of -2.0 μc. how many electrons must be removed so that the charge becomes +3.0 μ c?

Answer 1

Approximately 3.12 x 10¹³ electrons must be removed from an object with a charge of -2.0 μC to achieve a charge of +3.0 μC, utilizing the charge of an electron and the total charge change required.

Step-by-step explanation:

To determine how many electrons must be removed from an object with a charge of -2.0 μC to achieve a charge of +3.0 μC, we first need to note the total charge change required. The object initially has a negative charge which means it has excess electrons. To change from -2.0 μC to +3.0 μC, a total charge change of 5.0 μC is needed (since -2 + 5 = +3).

One electron has a charge of approximately -1.602 x 10-19 coulombs. Therefore, the number of electrons to be removed can be calculated using the formula:

Number of electrons = Total charge change/electron charge

Number of electrons = 5.0 μC / 1.602 x 10⁻¹⁹ C/e-

Since 1 μC = 1 x 10⁻⁶ C, we have:

Number of electrons = (5.0 x 10-6 C) / (1.602 x 10⁻¹⁹ C/e-)

Number of electrons ≈ 3.12 x 10¹³

Approximately 3.12 x 10¹³ electrons must be removed from the object to change its charge from -2.0 μC to +3.0 μC.

Answer 2

Each electron has a charge of
`e=-1.6 \cdot 10^(-19) C`

The initial charge of the object is
`Q_i = -2.0 \mu C=-2.0 \cdot 10^(-6) C`

The final charge of the object is
`Q_f = +3.0 \mu C=+3.0 \cdot 10^(-6)C`

So the change in charge of the object is

`\Delta Q = Q_i - Q_f =-2.0 \cdot 10^(-6) C-(3 \cdot 10^(-6) C)=-5.0 \cdot 10^(-6) C`

So, the number of electrons removed from the object is

`N=(\Delta Q)/(e)=(-5.0 \cdot 10^(-6) C)/(-1.6 \cdot 10^(-19)C)=3.13 \cdot 10^(13)`