For the given arrangement,where four charges | vedclass

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

Question

(D) Let the square lie in the $xy$-plane with its center at the origin. The vertical axis is the $z$-axis. The four corners are at $(\pm a/\sqrt{2}, \

Vedclass · Accepted Answer

$-4q$

Vedclass · Answer

(D) Let the square lie in the $xy$-plane with its center at the origin. The vertical axis is the $z$-axis. The four corners are at $(\pm a/\sqrt{2}, \pm a/\sqrt{2}, 0)$.Three corners have charge $q$,and one corner has charge $Q+q$.The electric field component along the $z$-axis due to a charge $q_i$ at distance $r_i$ from the axis is $E_{z,i} = \frac{k q_i z}{(r_i^2 + z^2)^{3/2}}$.For the three charges $q$,the sum of the vertical components is $E_{z,1+2+3} = \frac{3kqz}{(r^2 + z^2)^{3/2}}$.For the fourth charge $(Q+q)$,the vertical component is $E_{z,4} = \frac{k(Q+q)z}{(r^2 + z^2)^{3/2}}$.For the net field along the $z$-axis to be zero,$E_{z,1+2+3} + E_{z,4} = 0$.$3kq + (Q+q) = 0 \implies Q+q = -3q \implies Q = -4q$.

For the given arrangement,where four charges are fixed at the corners of a square as shown,find the value of the additional charge $Q$ to be placed on one of the vertices so that the component of the net electric field along the vertical symmetric axis is zero at every point on the vertical axis.

Similar Questions

The point charges $Q$ and $-2Q$ are placed at a distance $r$ apart. If the electric field at the location of $Q$ (point $A$) due to $-2Q$ is $\vec E$,then the electric field at the location of $-2Q$ (point $B$) due to $Q$ will be:

Calculate the electric field at the origin due to an infinite number of charges as shown in the figure.

$A$ uniformly charged semicircular arc of radius $r$ has linear charge density $\lambda$. What is the electric field at its centre? $(\epsilon_0 = \text{permittivity of free space})$

$A$ thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net electric field $\vec{E}$ at the centre $O$ is

The charges $2q, -q, -q$ are located at the vertices of an equilateral triangle. At the center of the triangle:

Vedclass Test Series

Exam Paper Generator

Online Exam Module