Three point charges of magnitude $5 \mu \mathrm{C}$, $0.16 \mu \mathrm{C}$ and $0.3 \mu \mathrm{C}$ are located at the vertices $\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}$ of a right angled triangle whose sides are $\mathrm{AB}=3 \mathrm{~cm}$, $\mathrm{BC}=3\sqrt{2} \mathrm{~cm}$ and $\mathrm{CA}=3 \mathrm{~cm}$ and point A is the right angle corner. Charge at point A experiences ______ N of electrostatic force due to the other two charges.

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Electrostatics

Three point charges of magnitude

5 μ C

0.16 μ C

and

0.3 μ C

are located at the vertices

A

B

C

of a right angled triangle whose sides are

AB = 3 cm

BC = 32 cm

and

CA = 3 cm

and point A is the right angle corner. Charge at point A experiences ______ N of electrostatic force due to the other two charges.

Answer: 17

The charge at A experiences forces from charges at B and C, which are perpendicular to each other (right angle at A).

Force due to charge at C:

F_{1} = \frac{k \times 5 \times 0.3 \times 1 0 ^{- 12}}{( 3 \times 1 0 ^{- 2} ) ^{2}} = \frac{9 \times 1 0 ^{9} \times 1.5 \times 1 0 ^{- 12}}{9 \times 1 0 ^{- 4}} = 15 N

Force due to charge at B:

F_{2} = \frac{9 \times 1 0 ^{9} \times 5 \times 0.16 \times 1 0 ^{- 12}}{9 \times 1 0 ^{- 4}} = 8 N

Net force (perpendicular components):

F = F_{1}^{2} + F_{2}^{2} = 1 5^{2} + 8^{2} = 289 = 17 N

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Integer answer