A charge is distributed with a linear density `lamda` over a rod of the length L placed along radius vector drawn from the point where a point charge q is located. The distance between q and the nearest point on linear charge is R. The electrical force experienced by the linear charge due to q is

Options

A. `(qlamdaL)/(4piepsilon_(0)R^(2))`
B. `(qlamdaL)/(4piepsilon_(0)R(R+L))`
C. `(qlamdaL)/(4piepsilon_(0)RL)`
D. `(qlamdaL)/(4piepsilon_(0)L^(2))`

Explanation

To solve the problem of finding the electrical force experienced by a linear charge due to a point charge, we can follow these steps:

### Step 1: Understand the Setup
We have a linear charge distributed over a rod of length \( L \) with a linear charge density \( \lambda \). This means that the total charge \( Q \) on the rod can be expressed as:
\[ Q = \lambda L \]
The rod is placed along a radius vector drawn from a point charge \( q \), and the distance from the point charge to the nearest point on the linear charge is \( R \).

### Step 2: Define the Electric Field Due to the Point Charge
The electric field \( E \) created by the point charge \( q \) at a distance \( R \) is given by Coulomb's law:
\[ E = \frac{k \cdot |q|}{R^2} \]
where \( k \) is Coulomb's constant, approximately \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

### Step 3: Calculate the Force on the Linear Charge
The force \( F \) experienced by the linear charge due to the electric field can be calculated using the formula:
\[ F = Q \cdot E \]
Substituting for \( Q \) and \( E \):
\[ F = (\lambda L) \cdot \left(\frac{k \cdot |q|}{R^2}\right) \]
Thus, the expression for the force becomes:
\[ F = \frac{k \cdot \lambda L \cdot |q|}{R^2} \]

### Final Expression
The electrical force experienced by the linear charge due to the point charge \( q \) is:
\[ F = \frac{k \cdot \lambda L \cdot |q|}{R^2} \]

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