Question

A system contains nine charges 1 uc, 2 pc, 3 pc.... 9 PC respectively. The total charge on the system will be
66 μC
45 C
25 UC
15 C​

Answer 1

Given:

A system consists of nine charges 1 micro-C , 2 micro-C ......, 9 micro-C.

To find:

Total charge in the system

Calculation:

Method 1 :

Total charge in the system will be equal to the algebraic addition of all the individual charges of the system.

Total charge = 1 + 2 + 3 + ...... + 9

=> Total charge = 45 $\mu C$

Method 2 :

The charges are in Arithmetic Progression , such that first number is 1 and common difference is 1.

Number of terms is 9 ;

Total charge = n/2 ( a + l )

=> Total charge = 9/2 ( 1 + 9)

=> Total charge = 9/2 × 10

=> Total charge = 45 $\mu C$

Hence , final answer is:

Total charge is 45 $\mu$C.