Question

In figure, two positive charges q₂ and q₃ fixed along the y axis, exert a net electric force in the + x direction on a charge q1 fixed along the x-axis. If a positive charge Q is added at (x, 0), the force on q₁

(a)

(b)

विकल्प

• shall increase along the positive x-axis.

• shall decrease along the positive x-axis.

• shall point along the negative x-axis.

• shall increase but the direction changes because of the intersection of Q with q₂ and q₃.

Answer 1

shall increase along the positive x-axis.

Explanation:

Total force acting on a given charge due to the number of charges is the vector sum of the individual forces acting on that charge due to all the charges.

Consider the number of charges Q₁, Q₂, Q₃, ... are applying force on a charge Q.

Net force in Q will be `vecF_("net") = vecF_1 + vecF_2 + ... vecF_(n - 1) + vecF_n`

We know that like charges repel and unlike charges attract. The net electrostatic force on the charge qx by the charges q₂ and q₃ is along the positive x-direction. Hence the nature of force between q₁, q₂ and q₁, q₃ should be attractive. It means qx should be negative. This can be represented by the figure given alongside:

Now a positive charge Q is placed at (x, 0), hence the nature of force between q₁ and Q (positive) will be attractive and the force on q₁ by the charge Q should be along the positive x-axis direction. Now we can say that the net force on the charge qx due to charges q₂, q₃ and Q should be along the same direction as given in the diagram alongside:

Now it is clear from the figure given above that the force on qx shall increase along the positive x-axis due to the presence of positive charge Q placed at (x, 0).