The equivalent capacitance of the system shown in the following circuitis

The angle between the electric lines of force and the equipotential surface is

Two point charges −q and +q are placed at a distance of L, as shown in the figure. The magnitude of electric field intensity at a distance R (R ≫ L) varies as:

The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constants \(\text{K}_1\, \text{and}\, \text{K}_2\) with thickness \(\displaystyle \frac{3}{8}\text{d}\) and \(\displaystyle \frac{d}{2}\), respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between plates.
If \(\text{K}_1\,=\,1.25\, \text{K}_2\), the value of \(\text{K}_1\) is:

A thin spherical shell is charged by some source. The potential difference between the two points C and P (in V ) shown in the figure is: (Take \( \frac{1}{4πϵ0} = 9 × 10^9 \) SI units)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: The potential (V) at any axial point, at 2 m distance (r) from the centre of the dipole of dipole moment vector \(\vec{P}\) of magnitude, 4 ×10⁻⁶Cm , is ± 9 × 10³V. (Take \(\frac{1}{4πϵ_0} = 9 × 10^9\) SI units).

Reason R: V = ± \(\frac{2P}{4πϵ_0r^2}\) where r is the distance of any axial point, situated at 2 m from the centre of the dipole. In the light of the above statements, choose the correct answer from the options given below:

In the following circuit, the equivalent capacitance betweenterminal A and terminal B is :

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then
A. the charge stored in it, increases.
B. the energy stored in it, decreases.
C. its capacitance increases.
D. the ratio of charge to its potential remains the same.
E. the product of charge and voltage increases.
Choose the most appropriate answer from the options given below:

A parallel plate capacitor is charged by connecting it to a battery through a resistor. If I is the current in the circuit, then in the gap between the plates:

An electric dipole is placed at an angle of \(30^\circ\) with an electric field of intensity \(2 × 10^5NC^{−1}\). It experiences a torque equal to 4 Nm. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm.

An electric dipole is placed as shown in the figure.

The electric potential in \(10^2\,V\) at point P due to dipole is (\(E_0 =\).permittivity of free space and \(\displaystyle \frac{1}{4πϵ_0}=k\) )

Two hollow conducting spheres of radii R₁ and R₂ (R₁ ≫ R₂) have equal charges. The potential would be

A capacitor of capacitance C = 900pF is charged fully by 100V battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900pF as shown in figure (b). The electrostatic energy stored by the system (b) is

The equivalent capacitance of the combination shown in the figure is

Two charged spherical conductors of radius R₁ and R₂ are connected by a wire. Then the ratio of surface charge densities of the spheres (σ₁/σ₂) is

A parallel plate capacitor has a uniform electric field ' \(\vec{F}\) ' in the space between the plates. If the distance between the plates is ' d ' and the area of each plate is ' A ', the energy stored in the capacitor is ( ε₀ = permittivity of free space)

Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

A capacitor of capacitance ' C ', is connected across an ac source of voltage V, given by \( \text{V}\, =\, V_0\, sin\, \omega t\). The displacement current between the plates of the capacitor, would then be given by

A spherical conductor of radius 10 cm has a charge of \(3.2 × 10^{−7} C\) distributed uniformly. What is the magnitude of electric field at a point 15cm from the centre of the sphere? \(\displaystyle \frac{1}{ 4\, \pi\, \epsilon_0} = 9 × 10^9 N m^2/C^2\))

In a certain region of space with volume 0.2 m³, the electric potential is found to be 5 V through out. The magnitude of electric field in this region is:

A short electric dipole has a dipole moment of \(16 \times 10^{−9}\) Cm. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of \(60^\circ\) with the dipole axis is : \(\displaystyle \left(\frac{1}{4πϵ_0} = 9 × 10^9 Nm^2/C^2\right)\)

The capacitance of a parallel plate capacitor with air as medium is 6µF . With the introduction of a dielectric medium, the capacitance becomes 30µF. The permittivity of the medium is:
(\(E_0 = 8.85 × 10^{−12}\,C^2N^{−1}m^{−2}\))

A hollow metal sphere of radius R is uniformly charged. The electricfield due to the sphere at a distance r from the centre

An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is

The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\vec{E}\). Due to the force q \(\vec{E}\), its velocity increases from 0 to 6 ms⁻¹ in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system

The diagrams below show regions of equipotential. A positive charge is moved from A to B in each diagram.

A capacitor of 2 μF is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is