A charge Q is distributed over a line of leng | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the linear charge density be $\lambda = Q/L$. Consider a small element $dx$ at a distance $x$ from the charge $q$. The force $dF$ on charge $q

Vedclass · Accepted Answer

$\frac{qQ}{4\pi \epsilon_0 (r^2 - (L/2)^2)}$

Vedclass · Answer

(B) Let the linear charge density be $\lambda = Q/L$. Consider a small element $dx$ at a distance $x$ from the charge $q$. The force $dF$ on charge $q$ due to this element is $dF = \frac{1}{4\pi \epsilon_0} \frac{q (\lambda dx)}{x^2}$.Integrating this from $x = r - L/2$ to $x = r + L/2$:$F = \int_{r - L/2}^{r + L/2} \frac{q \lambda}{4\pi \epsilon_0 x^2} dx$$F = \frac{q \lambda}{4\pi \epsilon_0} \left[ -\frac{1}{x} \right]_{r - L/2}^{r + L/2}$$F = \frac{q (Q/L)}{4\pi \epsilon_0} \left( \frac{1}{r - L/2} - \frac{1}{r + L/2} \right)$$F = \frac{qQ}{4\pi \epsilon_0 L} \left( \frac{(r + L/2) - (r - L/2)}{r^2 - (L/2)^2} \right)$$F = \frac{qQ}{4\pi \epsilon_0 L} \left( \frac{L}{r^2 - (L/2)^2} \right)$$F = \frac{qQ}{4\pi \epsilon_0 (r^2 - (L/2)^2)}$

$A$ charge $Q$ is distributed over a line of length $L$. Another point charge $q$ is placed at a distance $r$ from the centre of the line distribution. Then the force experienced by $q$ is

Similar Questions

Two charges $+80 \mu C$ and $+20 \mu C$ are separated by a distance $r$ in air. An unknown third charge $q$ is placed at the centre of the line joining the two charges. If the system of charges is in equilibrium,then the value of $q$ is:

An infinite number of charges,each of charge $1 \,\mu C$,are placed on the $x$-axis at coordinates $x = 1, 2, 4, 8, ... \infty$. If a charge of $1 \, C$ is kept at the origin,what is the net force acting on the $1 \, C$ charge in Newtons?

$F$ is the force between two identical charged particles placed at a distance $Y$ from each other. If the distance between the charges is reduced to half the previous distance,then the force between them becomes:

Two similar spheres having $+q$ and $-q$ charge are kept at a certain distance $r$. $A$ force $F$ acts between them. If another similar sphere having $+q$ charge is kept in the middle of the two spheres, then it experiences a force in magnitude and direction as:

If the distance between two equal point charges is doubled,what would happen to the force between them?

Vedclass Test Series

Exam Paper Generator

Online Exam Module