A body consists of five sections. Sections 1 and 2 have charge 3q each. Sections 4 and 5 have charges 2q and 4q respectively. What is the charge on section 3 if the total charge on the body is 9q?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −3q
Charge is a scalar. By the additivity of charges, the total charge of a body is the algebraic sum of the charges on its parts. Each charge is added with its proper sign.
Let the charge on section 3 be \( x \). Adding the charges of all five sections:
\( \begin{aligned} 3q+3q+x+2q+4q &= 9q \\ 12q+x &= 9q \\ x &= -3q \end{aligned} \)
The negative sign shows that section 3 carries a negative charge of magnitude \( 3q \).
NCERT (2026-27):
Additivity of Charges – “… If a system contains n charges q1, q2, q3, …, qn, then the total charge of the system is q1 + q2 + q3 + … + qn. Charge has magnitude but no direction, similar to mass. However, there is one difference between mass and charge. Mass of a body is always positive whereas a charge can be either positive or negative. Proper signs have to be used while adding the charges in a system.”