Solve
Guides
0
Question
Three charged particles $$A, B$$ and $$C$$ with charges $$-4q, 2q$$ and $$-2q$$ are present on the circumference of a circle of radius $$d$$. The charged particles $$A, C$$ and centre $$O$$ of the circle formed an equilateral triangle as shown in figure. Electric field at $$O$$ along x-direction is:
Open in App
Solution
Verified by Toppr
Correct option is B. $$\dfrac{\sqrt{3}q}{\pi \in_0d^2}$$
The electric field due to B will be in the direction of line joining B and O (or B and C) [Ref. image 1]
The electric field due to C will be in the direction of line joining O and C.
Net electric Field due to B and C along OC $$= \dfrac{k2q}{d^2} + \dfrac{k2q}{d^2} = \dfrac{k4q}{d^2}$$
Now, Electric field due to A along OA $$= \dfrac{k4q}{d^2}$$
Net Electric field along the x-axis is [Ref. image 2]
$$2 \left[\dfrac{k4q}{d^2}\cos 30^o\right] = \dfrac{k4\sqrt{3}q}{d^2}$$
$$= \dfrac{\sqrt{3}q}{\pi \in_0d^2}$$
The electric field due to C will be in the direction of line joining O and C.
Net electric Field due to B and C along OC $$= \dfrac{k2q}{d^2} + \dfrac{k2q}{d^2} = \dfrac{k4q}{d^2}$$
Now, Electric field due to A along OA $$= \dfrac{k4q}{d^2}$$
Net Electric field along the x-axis is [Ref. image 2]
$$2 \left[\dfrac{k4q}{d^2}\cos 30^o\right] = \dfrac{k4\sqrt{3}q}{d^2}$$
$$= \dfrac{\sqrt{3}q}{\pi \in_0d^2}$$
Was this answer helpful?
25
Similar Questions
Q1
Three charged particles $$A, B$$ and $$C$$ with charges $$-4q, 2q$$ and $$-2q$$ are present on the circumference of a circle of radius $$d$$. The charged particles $$A, C$$ and centre $$O$$ of the circle formed an equilateral triangle as shown in figure. Electric field at $$O$$ along x-direction is:
View Solution
Q2
Three charged particles A, B and, C with charge $ -4q, +2q and -2q$ are present on the circumference of a circle of radius $ d$. The charge particles A, C and centre O of the circle formed an equilateral triangle as shown in the figure. The electric field at O along $ x- direction$ is:
View Solution
Q3
Three equal point charges with charge +q each are moving along a circle of radius R and a fixed point charge −2q is placed at the centre of the circle. If +q charges are revolving at constant speed around −2q as shown, then the speed of charges are
(Assume that charges (+q) form vertices of equilateral triangle)
(Assume that charges (+q) form vertices of equilateral triangle)
View Solution
Q4
Charge q, 2q, 3q, and 4q are placed at the corners A, B, C and D of a square as shown in the following figure. The direction of electric field at the centre of the square is along
View Solution
Q5
Consider a system of three charges q/3,q/3,−2q/3 placed at points A, B and C respectively as shown in the figure. If the radius of the circle is R and ∠CAB is 60o, then the electric field at the centre O is
View Solution