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Electric Charges and Fields — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectric Charges and Fields1 Mark
Question
For two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false and R is also false.
Assertion (A): For charge to be in equilibrium, sum of the forces on charge due to rest of the two charges must be zero.
Reason (R): A charge is lying at the centre of the line joining two similar charges each which are fixed. The system will be in equilibrium if that charge is one fourth of the similar charges.
✓

Answer

  1. A is true but R is false.

Explanation:

According to Coulomb's law, $\text{F}=\text{k}\frac{\text{Q}_1\text{Q}_2}{\text{r}^2}.$

The force on q due to A,

$\text{F}_\text{A}=\frac{1}{4\pi\in_0}\cdot\frac{\text{Qq}}{(\frac{\text{r}}{2})^2}$ to the right

Due to B,

$\text{F}_\text{B}=\frac{1}{4\pi\in_0}\cdot\frac{\text{Qq}}{(\frac{\text{r}}{2})^2}$ to the right

$\therefore$ Their sum is zero whether q is $+\frac{\text{Q}}{4}$or $-\frac{\text{Q}}{4}$ or any other value.

Therefore, it is not true that the third charge has to be $\frac{\text{Q}}{4}$ only. It can be any value.

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