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1. Electric Charges and Fields
normal
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
A
$-$ $\frac{\lambda }{{2\pi {\varepsilon _0}R}}\,\hat i$
B
$\frac{\lambda }{{2\pi {\varepsilon _0}R}}\,\hat j$
C
$\frac{{\sqrt 2 \,\,\lambda }}{{4\pi {\varepsilon _0}R}}\,\hat i$
D
None
Solution
$E_{\mathrm{net}}=\sqrt{2} E=\sqrt{2}\left[\frac{\lambda \sqrt{2}}{4 \pi \in 0} R\right] \Rightarrow \vec{E}=\frac{\lambda(-\hat{i})}{2 \pi \in 0 R}$
Standard 12
Physics
