Question

An infinite long straight wire having a charge density λ is kept along y'y axis in x-y plane. The Coulomb force on a point charge q at a point P (x, 0) will be ______.

Options

• attractive and `(q lambda)/(2 pi epsilon_0x)`

• repulsive and `(q lambda)/(2 pi epsilon_0x)`

• attractive and `(q lambda)/(pi epsilon_0x)`

• repulsive and `(q lambda)/(2 pi epsilon_0x)`

Answer 1

An infinite long straight wire having a charge density λ is kept along y'y axis in x-y plane. The Coulomb force on a point charge q at a point P (x, 0) will be `bbunderline("repulsive and" (q lambda)/(2 pi epsilon_0x))`.

Explanation:

Electric field due to an infinite long straight wire having a charge density λ that is kept along y'y axis in x-y plane is given by 

`E = lambda/(2 pi epsilon_0 x)`

Now, Coulomb force acting on a point charge q at a point P(x, 0) will be

⇒ F = qE 

⇒ `F = (q lambda)/(2 pi epsilon_0 x)`

Given that the charge on q is positive and the charge density λ is similarly positive, it follows that like charges repel each other; thus, the Coulomb force will be repulsive in nature.