Question

Question 1.6: Four point charges qA = 2 μC, qB = −5 μC, qC = 2 μC, and qD = −5 μC are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 μC placed at the centre of the square?
Class 12 - Physics - Electric Charges And Fields Electric Charges And Fields Page-46t

Answer 1

Solution:

in this problem  Four point charges qA = 2 µC, qB = −5 µC, qC = 2 µC, and qD = −5 µC are located at the corners of a square ABCD of side 10 cm.

Given that

 A square ABCD  with each side = 10 cm  = 0.1 m (divide by 100 to convert cm to m )

Charge qA = 2 µC, qB = −5 µC, qC = 2 µC, and qD = −5

And 1 µC placed at the centre of the square

Draw the figure

 

Apply Coulomb’s law



q1 = first charge

q2 = Second charge

r = distance between both charge

ε0= permittivity of free space

We know that OA = OC hence  

FOA = - FOC

FOA + FOC  = 0

Similarly  

FOB + FODC  = 0

Similarly other forces will also cancel out to each other

FTOTAL =0

Hence sum of all forces will =0

Answer 2

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The given figure shows a square of side 10 cm with four charges placed at its corners.

O is the centre of the square.

Where,

(Sides) AB = BC = CD = AD = 10 cm

(Diagonals) AC = BD = cm

AO = OC = DO = OB = cm

A charge of amount 1μC is placed at point O.

Force of repulsion between charges placed at corner A and centre O is equal in magnitude but opposite in direction relative to the force of repulsion between the charges placed at corner C and centre O.

Hence, they will cancel each other.

Similarly, force of attraction between charges placed at corner B and centre O is equal in magnitude but opposite in direction relative to the force of attraction between the charges placed at corner D and centre O.

Hence, they will also cancel each other.

Therefore, net force caused by the four charges placed at the corner of the square on 1 μC charge at centre O is zero.

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