Question
Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is $30^{\circ} .$ The electric field in the region shown between them is given by
✓
Answer
Electric field due to each sheet is uniform and equal to $\mathrm{E}=\frac{\sigma}{2 \varepsilon_{0}}$
Now net electric field between plates
$\overrightarrow{\mathrm{E}}_{\mathrm{net}} =\mathrm{E} \cos 60^{\circ}(-\hat{\mathrm{x}})+\left(\mathrm{E}-\mathrm{E} \sin 60^{\circ}\right)(\hat{\mathrm{y}})$
$=\frac{\sigma}{2 \varepsilon_{0}}\left[-\frac{\hat{\mathrm{x}}}{2}+\left(1-\frac{\sqrt{3}}{2}\right) \hat{\mathrm{y}}\right]$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Flux passing through loop is proportional to
A astronomical telescope has objective and eyepiece of focal lengths $40\,\, cm$ and $4\,\, cm$ respectively. To view an object $200\,\, cm$ away from the objective, the lenses must be separated by a distance.....$cm$
→The liquid meniscus in capillary tube will be convex, if the angle of contact is
In a playground there is a merry-go-round of mass $120\ kg$ and radius $4\ m$. The radius of gyration is $3\ m$. A child of mass $30\ kg$ runs at a speed of $5\ m/sec$ tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglect friction and find the angular velocity of the merry-go-round and child ......... $ rad/sec$.
→A constant force acts on a body. Which of the following correctly represents the variation of the power $P$ developed with time $t$?
→When unpolarized light is incident at an angle of $60^{\circ}$ on a transparent medium from air. The reflected ray is completely polarized. The angle of refraction in the medium is
→Unit of moment of inertia in $MKS$ system
→In a Young's double slit experiment, the separation between the two slits is $d$ and the wavelength of the light is $\lambda$. The intensity of light falling on slit $1$ is four times the intensity of light falling on slit $2$. Choose the correct choice$(s)$.
→$(A)$ If $\mathrm{d}=\lambda$, the screen will contain only one maximum
$(B)$ If $\lambda<\mathrm{d} < 2 \lambda$, at least one more maximum (besides the central maximum) will be observed on the screen
$(C)$ If the intensity of light falling on slit $1$ is reduced so that it becomes equal to that of slit $2$ , the intensities of the observed dark and bright fringes will increase
$(D)$ If the intensity of light falling on slit $2$ is increased so that it becomes equal to that of slit $1$ , the intensities of the observed dark and bright fringes will increase
A body of mass $m_1$ exerts a force on another body of mass $m_2$. If the magnitude of acceleration of $m_2$ is $a_2$, then the magnitude of the acceleration of $m_1$ is (considering only two bodies in space)
→Space between two concentric conducting spheres of radii $a$ and $b (b > a)$ is filled with $a$ medium of resistivity $\rho $. The resistance between the two spheres will be
→