Question

A system contains 9 charges 1uC, 2uC, 3uC....9uC respectively. The total charge on the system will be

Answer 1

Answer:

0.000045 is the total charge

Step by step:

How to convert microcoulombs to coulombs

1C = 1000000μC

or

1μC = 0.000001C

Microcoulombs to coulombs formula

The charge in coulombs Q(C) is equal to the charge in microcoulombs Q(μC) divided by 1000000:

Q(C) = Q(μC) / 1000000

*****add all of the 9 charges in your question u get 45uC

Q(C)=45/  1000000

Q(C)=0.000045

hope this is correct!

Answer 2

Given:

A system contains 9 charges with values 1 uC, 2uC......9uC.

To find:

Total charge of the system.

Calculation:

Method 1:

The total charge on the system can be calculated by algebraic addition of the individual charges of the system.

Net charge = 1+2+3+4+5+6+7+8+9 = 45 micro-C.

Method 2:

The formula of Arithmetic Progression can be used to calculate the total charge of the system.

Series: 1,2,3.....9

First term = 1 = a

Difference = 1 = d

Number of terms = 9 = n

$net \: charge = \dfrac{n}{2} \{2a + (n - 1)d \}$

$= > net \: charge = \dfrac{9}{2} \{(2 \times 1) + (9 - 1)1\}$

$= > net \: charge = \dfrac{9}{2} \{2 + 8\}$

$= > net \: charge = \dfrac{9}{2} \{10\}$

$= > net \: charge = 45 \: \mu C$

So final answer is

$\boxed{ \sf{ net \: charge = 45 \: \mu C }}$