MCQ
The charge per unit length of the four quadrant of the ring is $2\ \lambda , - 2\ \lambda , \lambda$ and $- \lambda$ respectively. The electric field at the centre is
  • $-$ $\frac{\lambda }{{2\pi {\varepsilon _0}R}}\,\hat i$
  • B
    $\frac{\lambda }{{2\pi {\varepsilon _0}R}}\,\hat j$
  • C
    $\frac{{\sqrt 2 \,\,\lambda }}{{4\pi {\varepsilon _0}R}}\,\hat i$
  • D
    None

Answer

Correct option: A.
$-$ $\frac{\lambda }{{2\pi {\varepsilon _0}R}}\,\hat i$
a
$E_{\mathrm{net}}=\sqrt{2} E=\sqrt{2}\left[\frac{\lambda \sqrt{2}}{4 \pi \in 0} R\right] \Rightarrow \vec{E}=\frac{\lambda(-\hat{i})}{2 \pi \in 0  R}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

In the circuit shown, what is the potential difference $V_{PQ}$? ................ $V$
The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is $6\,V$ and the load resistance is $R_L= 4\,k\Omega .$ The series resistance of the circuit is $R_i = 1\,k\Omega .$ If the battery voltage $V_B$ varies from $8\,V$ to $16\,V,$ what are the minimum and maximum values of the current through Zener diode?
In a transistor:
A capacitor of capacity C has charge Q and stored energy is W. If the charge is increased to 2Q, the stored energy will be
Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2 - V_1 = 20\ V$. (i.e., plate $2$ is at a higher potential). The plates are separated by $d = 0.1\ m$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1. $ What is its speed when it hits plate $2?$
$(e = 1.6 \times 10^{-19}\ C, m_e= 9.11 \times 10^{-31}\ kg)$
The average binding energy per nucleon is maximum for the nucleus:
A lamp is hanging along the axis of a circular table of radius $r.$ At what height should the lamp be placed above the table, so that the illuminance at the edge of the table is $\frac{1}{8}$ of that at its center
For a convex lens the distance of the object is taken on $X$-axis and the distance of the image is taken on $Y$-axis, the nature of the graph so obtained is
In nuclear reactions, we have the conservation of
The magnetic moment of a circular orbit of radius $‘r’$ carrying a charge $‘q’$ and rotating with velocity $v$ is given by