Two point charges and are placed at points and respectively. Force on charge is N.

Question

Two point charges $q_{1} = 3 μ C$ and $q_{2} = - 4 μ C$ are placed at points $(2 \hat{i} + 3 \hat{j} + 3 \hat{k})$ and $(\hat{i} + \hat{j} + \hat{k})$ respectively. Force on charge $q_{2}$ is _____ N.

(Take $\frac{1}{4 π ε_{0}} = 9 \times 10^{9}$ SI units) [2026]

Smart Achievers · Accepted Answer

(2)

$The force on charge q_{2} due to charge q_{1} ({\vec{F}}_{21}) is given by$ $Coulomb's Law in vector form:$

${\vec{F}}_{21} = \frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{| {\vec{r}}_{21} |^{3}} {\vec{r}}_{21}$

$\frac{1}{4 π ε_{0}} = 9 \times 10^{9}$

${\vec{r}}_{21} = (\hat{i} + \hat{j} + \hat{k}) - (2 \hat{i} + 3 \hat{j} + 3 \hat{k}) = - (\hat{i} + 2 \hat{j} + 2 \hat{k}) m$

${\vec{F}}_{21} = [\frac{(9 \times 10^{9}) (3 \times 10^{- 6}) (- 4 \times 10^{- 6})}{3^{3}}] [- (\hat{i} + 2 \hat{j} + 2 \hat{k})] N$

$\Rightarrow {\vec{F}}_{21} = (4 \hat{i} + 8 \hat{j} + 8 \hat{k}) \times 10^{- 3} N$

Solution

Q.
Two point charges $q_{1} = 3 μ C$ and $q_{2} = - 4 μ C$ are placed at points $(2 \hat{i} + 3 \hat{j} + 3 \hat{k})$ and $(\hat{i} + \hat{j} + \hat{k})$ respectively. Force on charge $q_{2}$ is _____ N.

(Take $\frac{1}{4 π ε_{0}} = 9 \times 10^{9}$ SI units) [2026]

1 $(12 \hat{i} + 24 \hat{j} + 24 \hat{k}) \times 10^{- 3}$

2 $(4 \hat{i} + 8 \hat{j} + 8 \hat{k}) \times 10^{- 3}$

3 $(3 \hat{i} + 6 \hat{j} + 6 \hat{k}) \times 10^{- 3}$

4 $(- 4 \hat{i} - 8 \hat{j} - 8 \hat{k}) \times 10^{- 3}$

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Solution

Q. Two point charges q1=3 μC and q2=-4 μC are placed at points (2i^+3j^+3k^) and (i^+j^+k^) respectively. Force on charge q2 is _____ N. (Take 14πε0=9×109 SI units) [2026]

1 (12i^+24j^+24k^)×10-3

2 (4i^+8j^+8k^)×10-3

3 (3i^+6j^+6k^)×10-3