Point charges having values + 0.1 μC, + 0.2 μC, – 0.3 μC and –0.2 μC are placed at the corners A, B, C and D respectively of a square of side one metre. Calculate the magnitude of the force on a charge of + 1 μC placed at the centre of the square.

Solution

Using the above fig.

${AC}^{2} = {AB}^{2} + {BC}^{2} = 1 + 1 = 2$

$\Rightarrow$ $AC = \sqrt{2} m$
$AO = \frac{1}{2} \sqrt{2} m = 0.5 \sqrt{2} m$
Also, $AO = CO = BO = DO = 0.5 \sqrt{2} m$

Let F_a be the force exerted by the charge of ‘+ O.1μC’ on the charge ‘+ 1 μC’ placed at centre O of the square.
Then using Coulomb's law for Electrostatic force,

$F_{A} = 9 \times 10^{9} {Nm}^{2} C^{- 2} \frac{(0.1 \times 10^{- 6} C) (1 \times 10^{- 6} C)}{2 (0.5)^{2} m^{2}}$
$\Rightarrow$ $F_{A} = \frac{9 \times 10^{9} \times 0.1 \times 10^{- 12}}{2 \times 0.25} N = 0.0018 N$

If F_c is the force exerted by charge at C on charge at O, then
$F_{C} = 9 \times 10^{9} \frac{(0.3 \times 10^{- 6}) (1 \times 10^{- 6})}{2 (0.5)^{2}} N = \frac{9 \times 0.3 \times 10^{- 3}}{2 \times 0.25} N = 0.0054 N$

Both $F_{A} and F_{C}$ act in the same direction. The resultant of $F_{A} and F_{C},$

$F_{1} = (0.0018 + 0.0054) N = 0.0072 N$

Force exerted by the charge at B on the charge at O,

$F_{B} = 9 \times 10^{9} \frac{(0.2 \times 10^{- 6}) (1 \times 10^{- 6})}{2 (0.5)^{2}} N$

$= 3.6 \times 10^{- 3} N = 0.0036 N$

Force exerted by the charge at D on the charge at O,
$F_{D} = 9 \times 10^{9} \frac{(0.2 \times 10^{- 6}) (1 \times 10^{- 6})}{2 (0.5)^{2}} N = 0.0036 N$

Both $F_{B} and F_{D}$ act in the same direction.
Resultant of $F_{B} and F_{D'}$
$F_{2} = (0.0036 + 0.0036) N = 0.0072 N$

The angle between F₁ and F₂ is clearly 90°.
So, the resultant F of F₁ and F₂ is given by

$F = \sqrt{(0.0072)^{2} + (0.0072)^{2}} N = 0.0072 \sqrt{2} N = 0.0072 \times 1.414 N = 0.01018 N$

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Electric Charges And Fields

Point charges having values + 0.1 μC, + 0.2 μC, – 0.3 μC and –0.2 μC are placed at the corners A, B, C and D respectively of a square of side one metre. Calculate the magnitude of the force on a charge of + 1 μC placed at the centre of the square.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

Point charges having values + 0.1 μC, + 0.2 μC, – 0.3 μC and –0.2 μC are placed at the corners A, B, C and D respectively of a square of side one metre. Calculate the magnitude of the force on a charge of + 1 μC placed at the centre of the square.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?