Two charges of 25uc and 36uc are placed 10cm apart from each other then the force on the charge q will be zero when it is placed at a distance of..?
Answers
Answer:
Two charges of 25uc and 36uc are placed 10cm apart from each other then the force on the charge q will be zero when it is placed at a distance of..?
Answer : the force on the charge q will be zero when it is placed at a distance 4.5cm from charge 25μC.
Explanation:
Two charges of 25μC and 36μC are placed 10cm apart from each other. Suppose a point P, on line the two charges, distance from one charge is x cm, where electric field intensity becomes zero.
as we know
electric field intensity due to at Point charge =
k(25μC) / x² = k(36μC) / (10 - x)²
⇒ 25 / x² = 36 / (10 - x)²
⇒ 5² / x² = 6² / (10 - x)²
⇒ 5 / x = 6/(10 - x)
⇒ 5(10 - x) = 6x
⇒ 50 = 11x => x = 55 / 11 = 4.5
Therefore the force on the charge q will be zero when it is placed at a distance 4.5cm from charge 25μC.
Given :
The magnitude of two charges are = = 25 c
= 36 c
The distance between two charges = 10 cm
To Find :
The distance at which charge is placed when the force on the charge q will be zero
Solution ;
Let The distance of charge from point p = x cm
So, The distance of charge from point p = ( 10 - x ) cm
Now,
Electric force at any point at d distance is given as , F = k
where k = 9 ×
So, Force due to charge = k
And Force due to charge = k
And , Force due to charge = Force due to charge
i.e k = k
Or, =
Or, 25 ( 10 - x)² = 36 × x²
O, 25 [ 100 + x² - 20 x ] = 36 × x²
Or, 2500 + 25 × x² - 200 x = 36 × x²
Or, 36 × x² - 25 × x² + 200 x - 2500 = 0
Or, 9 × x² + 200 x - 2500 = 0
now, Solving this quadratic equation
x =
∴ x = 8.9 cm , - 31.14 cm
So, The distance = x = 8.9 cm