1
WB JEE 2024
+1
-0.25

A charge Q is placed at the centre of a cube of sides a. The total flux of electric field through the six surfaces of the cube is

A
$$\frac{6 \mathrm{Qa}^2}{\epsilon_0}$$
B
$$\frac{\mathrm{Q} \mathrm{a}^2}{6 \epsilon_0}$$
C
$$\mathrm{Q} / \epsilon_0$$
D
$$\mathrm{Q} \mathrm{a}^2 / \epsilon_0$$
2
WB JEE 2024
+1
-0.25

Three point charges $$\mathrm{q},-2 \mathrm{q}$$ and $$\mathrm{q}$$ are placed along $$x$$ axis at $$x=-{a}, 0$$ and $a$ respectively. As $$\mathrm{a} \rightarrow 0$$ and $$\mathrm{q} \rightarrow \infty$$ while $$\mathrm{q} \mathrm{a}^2=\mathrm{Q}$$ remains finite, the electric field at a point P, at a distance $$x(x \gg a)$$ from $$x=0$$ is $$\overrightarrow{\mathrm{E}}=\frac{\alpha \mathrm{Q}}{4 \pi \epsilon_0 x^\beta} \hat{i}$$. Then

A
$$\alpha=\beta$$
B
$$\alpha=2 \beta$$
C
$$\alpha=\frac{2}{3} \beta$$
D
$$2 \alpha=3 \beta$$
3
WB JEE 2023
+1
-0.25

Consider a positively charged infinite cylinder with uniform volume charge density $$\rho > 0$$. An electric dipole consisting of + Q and $$-$$ Q charges attached to opposite ends of a massless rod is oriented as shown in the figure. At the instant as shown in the figure, the dipole will experience,

A
a force to the left and no torque.
B
a force to the right and a clockwise torque.
C
a force to the right and a counter clockwise torque.
D
no force but only a clockwise torque.
4
WB JEE 2023
+1
-0.25

A thin glass rod is bent in a semicircle of radius R. A charge is non-uniformly distributed along the rod with a linear charge density $$\lambda=\lambda_0\sin\theta$$ ($$\lambda_0$$ is a positive constant). The electric field at the centre P of the semicircle is,

A
$$-\frac{\lambda_{o}}{8 \pi \varepsilon_{o} R} \hat{j}$$
B
$$\frac{\lambda_{o}}{8 \pi \varepsilon_{o} R} \hat{j}$$
C
$$\frac{\lambda_{\mathrm{o}}}{8 \pi \varepsilon_{\mathrm{o}} \mathrm{R}} \hat{\mathrm{i}}$$
D
$$-\frac{\lambda_{\mathrm{o}}}{8 \pi \varepsilon_{\mathrm{o}} R} \hat{\mathrm{i}}$$
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