1
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
$$2 \alpha=3 \beta$$
2
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.
3
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
$$-\frac{\lambda_{\mathrm{o}}}{8 \pi \varepsilon_{\mathrm{o}} R} \hat{\mathrm{i}}$$
4
WB JEE 2023
+1
-0.25

The figure represents two equipotential lines in x-y plane for an electric field. The x-component E$$_x$$ of the electric field in space between these equipotential lines is,

A
100 V/m
B
$$-$$100 V/m
C
200 V/m
D
$$-$$200 V/m
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