1
KCET 2023
+1
-0

A positively charged glass rod is brought near uncharged metal sphere, which is mounted on an insulated stand. If the glass rod is removed, the net charge on the metal sphere is

A
negative charge
B
zero
C
$$1.6 \times 10^{-19} \mathrm{C}$$
D
positive charge
2
KCET 2023
+1
-0

In the situation shown in the diagram, magnitude, if $$q < < |Q|$$ and $$r >>>a$$. The net force on the free charge $$-q$$ and net torque on it about $$O$$ at the instant shown are respectively.

($$p=2 a Q$$ is the dipole moment)

A
$$\frac{1}{4 \pi \varepsilon_0} \frac{p q}{r^3} \hat{\mathbf{i}},-\frac{1}{4 \pi \varepsilon_0} \frac{p q}{r^2} \hat{\mathbf{k}}$$
B
$$\frac{1}{4 \pi \varepsilon_0} \frac{p q}{r^2} \hat{\mathbf{k}}, \frac{1}{4 \pi \varepsilon_0} \frac{p q}{r^3} \hat{\mathbf{i}}$$
C
$$-\frac{1}{4 \pi \varepsilon_0} \frac{p q}{r^2} \hat{\mathbf{k}},-\frac{1}{4 \pi \varepsilon_0} \frac{p q}{r^3} \hat{\mathbf{i}}$$
D
$$\frac{1}{4 \pi \varepsilon_0} \frac{p q}{r^3} \hat{\mathbf{i}},+\frac{1}{4 \pi \varepsilon_0} \frac{p q}{r^2} \hat{\mathbf{k}}$$
3
KCET 2023
+1
-0

A uniform electric field vector $$\mathbf{E}$$ exists along horizontal direction as shown. The electric potential at $$A$$ is $$V_A$$. A small point charge $$q$$ is slowly taken from $$A$$ to $$B$$ along the curved path as shown. The potential energy of the charge when it is at point $$B$$ is

A
$$q\left[V_A-E x\right]$$
B
$$q\left[V_A+E x\right]$$
C
$$q\left[E x-V_A\right]$$
D
$$q E x$$
4
KCET 2023
+1
-0

A cubical Gaussian surface has side of length $$a=10 \mathrm{~cm}$$. Electric field lines are parallel to $$X$$-axis as shown in figure. The magnitudes of electric fields through surfaces $$A B C D$$ and $$E F G H$$ are $$6 ~\mathrm{kNC}^{-1}$$ and $$9 \mathrm{~kNC}^{-1}$$ respectively. Then, the total charge enclosed by the cube is

[Take, $$\varepsilon_0=9 \times 10^{-12} \mathrm{~Fm}^{-1}$$ ]

A
$$-0.27$$ nC
B
1.35 nC
C
$$-1.35$$ nC
D
0.27 nC
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