Question

Four charges are placed on the circumference
of a circle of radius R, 90° apart as shown in
the figure. The electric field strength at the
centre of the circle is:
Y.20
+30
+0
o
T-20​

Answer 1

Answer:

7:30

Explanation:

Given,

Four charges are placed on the circumference of a circle of radius R, 90° apart.

To Find,

The electric strength at the centre of the circle.

Concept:

First, we will consider the charges placed in the x-axis and the force which they are applying on the charge present at the center.

The force acting on a charged particle due to another charged particle is given by the following relation:

$F=k\frac{q_{1}q_{2} }{r^{2} } .r vector$, where q1,q2 are the magnitude of charges on the particles, r is the distance between them and K is a constant, and r vector is the direction vector which gives the direction.

Here,

The magnitude of the charges present at the circumference of the dial is the same, therefore we only have to calculate the direction of the forces.

Since,

The charge present in the center of the direct is a positive charge, the charge present at the 12 o'clock position and the 3 o'clock position will repel it. And the charge present at the 9 o'clock position and the 6 o'clock position will attract it.

The direction of the forces applied by the charge present at the circumference to the charge present at the center can be explained with the diagram given below:

The forces acting on the charge can be recorded in the x and y axis and it will be as shown below:

Now,

We have to find the resultant of the two forces acting in the direction of x and y axis, if we represent the direction of the resultant of the two forces, we will get the direction which is shown in the figure below:

Therefore,

We now have the direction of the resultant of the force acting on the charge placed at the center due to the charges present at the circumference.

If we consider that the hour hand is placed in this direction, then the hour hand must be pointing at a value between 6 and 9 hours, if we try to find an option which is between 6 and 9 hours it is the option B which is 7:30.

Hence, the correct answer is 7:30.

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Answer 2

Concept:

• Electric field strength

Given:

• + 3Q at 0°
• -2Q at 90°
• +Q at 180°
• +2Q at 270°

Find:

• The electric field strength at the centre of the circle

Solution:

E₁ = k3Q/R²

E₂ = -k2Q/R²

E₃ = kQ/R²

E₄ = k2Q/R²

E on y-axis = E₂ +E₄ = k2Q/R² + k2Q/R² = k4Q/R²

E on x-axis = E₁ +E₃ = k3Q/R² - kQ/R² = k2Q/R²

Net E = $\sqrt{Ey^{2} +Ex^{2} }$

Net E = $\sqrt{(k4Q/R²)^{2} +(k2Q/R²)^{2} }$

Net E = 2kQ √5/R²

tan theta = (k4Q/R²)/k2Q/R² = 2

theta = arctan 2 with the x axis

The electric field at the centre of the circle is 2kQ√5/R².

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