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Two shorts dipoles (A, B), A having charges \( \pm 2 \, \mu \text{C} \) and length \( 1 \, \text{cm} \) and B having charges \( \pm 4 \, \mu \text{C} \) and length \( 1 \, \text{cm} \) are placed with their centres \( 80 \, \text{cm} \) apart as shown in the figure. The electric field at a point P, equi-distant from the centres of both dipoles is _______ \( \text{N/C} \).

Two point charges \( 8\,\mu\text{C} \) and \( -2\,\mu\text{C} \) are located at \( x = 2 \, \text{cm} \) and \( x = 4 \, \text{cm} \), respectively on the \( x \)-axis. The ratio of electric flux due to these charges through two spheres of radii \( 3 \, \text{cm} \) and \( 5 \, \text{cm} \) with their centers at the origin is ______.

A simple pendulum has a bob with mass $m$ and charge $q$. The pendulum string has negligible mass. When a uniform and horizontal electric field $\vec{E}$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is _________. ($g$: acceleration due to gravity)

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field \( \vec{E}_1 = E_0 \hat{k} \). If another electric field \( \vec{E}_2 = 2E_0(\hat{y} + \hat{z}) \) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

Consider two identical metallic spheres of radius \( R \) each having charge \( Q \) and mass \( m \). Their centers have an initial separation of \( 4R \). Both the spheres are given an initial speed of \( u \) towards each other. The minimum value of \( u_0 \), so that they can just touch each other is:
\( \text{( Take } k = \dfrac{1}{4\pi \varepsilon_0} \text{ and assume } kQ^2 > G m^2 \text{ where } G \text{ is the Gravitational constant )} \)

A three coulomb charge moves from the point \( (0,-2,-5) \) to the point \( (5,1,2) \) in an electric field expressed as \( \vec{E} = 2x\,\hat{i} + 3y^{2}\,\hat{j} + 4\,\hat{k}\ \mathrm{N/C} \). The work done in moving the charge is ______ \( \text{J} \).

A point charge of \( 10^{-8} \, \text{C} \) is placed at origin. The work done in moving a point charge \( 2 \, \mu \text{C} \) from point \( A(4, 4, 2) \, \text{m} \) to \( B(2, 2, 1) \, \text{m} \) is ______________ \( \text{J} \). \( \left( \frac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^{9} \text{ in SI units} \right) \)

A point charge \( q = 1 \, \mu \text{C} \) is located at a distance \( 2 \, \text{cm} \) from one end of a thin insulating wire of length \( 10 \, \text{cm} \) having a charge \( Q = 24 \, \mu \text{C} \), distributed uniformly along its length, as shown in figure. Force between \( q \) and wire is ______________ \( \text{N} \).
(Use: \( \dfrac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^{9} \, \text{N m}^{2} / \text{C}^{2} )\)

Five positive charges each having charge \( q \) are placed at the vertices of a pentagon as shown in the figure. The electric potential \( (V) \) and the electric field \( (\vec{E} )\) at the center \( O \) of the pentagon due to these five positive charges are:

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubbles is:

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

Assertion A: In electrostatics, a conductor does not store any net charge inside.

Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift.

Choose the correct answer from the options given below:

A thin half ring of radius \( 35 \, \text{cm} \) is uniformly charged with a total charge of \( Q \) coulomb. If the magnitude of the electric field at centre of the half ring is \( 100 \, \text{V/m} \), then the value of \( Q \) is _____ \( \text{nC} \). \( (\varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 / \text{Nm}^2 \) and \( \pi = 3.14) \)

The electric potential as a function of \( x, y \) is given by \( V = 5(x^{2} - y^{2}) \, \text{V} \). The electric field at a point \( (2, 3) \, \text{m} \) is ______ \( \text{V/m} \).

Two charged conducting spheres \( S_1 \) and \( S_2 \) of radii \( 8 \, \text{cm} \) and \( 18 \, \text{cm} \) are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on \( S_1 \) and \( S_2 \) spheres are \( E_{S1} \) and \( E_{S2} \) respectively. The value of \( \frac{E_{S1}}{E_{S2}} \) is ______.

Two-point charges \( 2q \) and \( q \) are placed at vertex \( A \) and centre of face \( CDEF \) of the cube as shown in figure. The electric flux passing through the cube is:

There are three co-centric conducting spherical shells \( A, B \) and \( C \) of radii \( a, b \) and \( c \) respectively \( (c>b>a) \) and they are charged with charge \( q_1, q_2 \) and \( q_3 \) respectively. The potentials of the spheres \( A, B \) and \( C \) respectively, are:

Two point charges \( q_1 = 3\,\mu\text{C} \) and \( q_2 = -4\,\mu\text{C} \) are placed at points \( (2\hat{i}+3\hat{j}+3\hat{k}) \) and \( (\hat{i}+\hat{j}+\hat{k}) \) respectively. Force on charge \( q_2 \) is ______ \( \text{N} \). [Take \( \dfrac{1}{4\pi \varepsilon_0} = 9\times 10^{9} \) SI units]

Six point charges are kept $60^\circ$ apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is ________. ($\epsilon_0$ is permittivity of free space)

The electrostatic potential in a charged spherical region of radius \( r \) varies as \( V = ar^3 + b \), where \( a \) and \( b \) are constants. The total charge in the sphere of unit radius is \( \alpha \times \pi a \varepsilon_0 \). The value of \( \alpha \) is ______. (permittivity of vacuum is \( \varepsilon_0 \))

Electric field in a region is given by \( \vec{E}=Ax\,\hat{i}+By\,\hat{j} \), where \( A=10 \, \mathrm{V/m^{2}} \) and \( B=5 \, \mathrm{V/m^{2}} \). If the electric potential at a point \( (10,20) \) is \( 500 \, \mathrm{V} \), then the electric potential at origin is ______ \( \mathrm{V} \).

Two short electric dipoles A and B having dipole moment \( p_1 \) and \( p_2 \) respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point \( x \) is making an angle of \( 60^\circ \) with the line joining points \( O \) and \( x \). The ratio of the dipole moments \( \frac{p_2}{p_1} \) is ______.

Three charges \( +2q, +3q \) and \( -4q \) are situated at \( (0,-3a) \), \( (2a,0) \), \( (-2a,0) \) respectively in the \( xy \) plane. The resultant dipole moment about origin is ______.

Two metal plates (A, B) are kept horizontally with separation of \( \left( \dfrac{12}{\pi} \right) \, \text{cm} \), with plate A on the top. An atomizer jet sprays oil (density \( 1.5 \, \text{g/cm}^3 \)) droplets of radius \( 1 \, \text{mm} \) horizontally. All oil droplets carry a charge \( 5 \, \text{nC} \). The potentials \( V_A \) and \( V_B \) are required on plates A and B respectively in order to ensure the droplets do not descend. The values of \( V_A \) and \( V_B \) are ______. (Neglect the air resistance to the droplets and take \( g = 10 \, \text{m/s}^2 \))

A particle having charge \( 10^{-9}\, \text{C} \) moving in \( x\text{-}y \) plane in fields of \( 0.4\,\hat{\jmath}\, \text{N/C} \) and \( 4\times 10^{-3}\,\hat{k}\, \text{T} \) experiences a force of \( (4\hat{\imath}+2\hat{\jmath})\times 10^{-10}\, \text{N} \). The velocity of the particle at that instant is __________ \( \text{m/s} \).

Two charges \( 7 \, \mu \text{C} \) and \( -2 \, \mu \text{C} \) are placed at \( (-9, 0, 0) \, \text{cm} \) and \( (9, 0, 0) \, \text{cm} \) respectively in an external field \( {E} = \dfrac{A}{r^2} \, \hat{r} \), where \( A = 9 \times 10^{5} \, \text{N}/\text{C} \cdot \text{m}^{2} \). Considering the potential at infinity is \( 0 \), the electrostatic energy of the configuration is ______ \( \text{J} \).

Two point charges of \( 1 \, \text{nC} \) and \( 2 \, \text{nC} \) are placed at the two corners of equilateral triangle of side \( 3 \, \text{cm} \). The work done in bringing a charge of \( 3 \, \text{nC} \) from infinity to the third corner of the triangle is ________ \( \mu \text{J} \).
\( \dfrac{1}{4\pi\varepsilon_{0}} = 9 \times 10^{9} \, \text{N}\cdot\text{m}^{2}\,/\text{C}^{2} \)

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JEE Main 2026 22nd Jan Evening Shift

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubbles is: