A wire (area 10^-4 m²) forms a 30 cm ring. Charge 2πC is spread uniformly over the ring, and 30 pC sits at its centre. The ring tension is ____ N (no deformation, gravity neglected; 1/(4πε₀) = 9 × 10⁹ SI units).

An electric charge 10^-6 μC is placed at origin (0, 0) m of X-Y co-ordinate system. Two points P and Q are situated at (√3, √3) m and (√6, 0) m respectively. The potential difference between the points P and Q will be :

Two charges −4 μC and +4 μC are placed at the points A(1, 0, 4)m and B(2, −1, 5)m located in an electric field E⃗ = 0.20 î V/cm. The magnitude of the torque acting on the dipole will be (Use √2 = 1.41)

Assertion A: work done by the electric field in moving a positive charge on an equipotential surface is always zero. Reason R: electric field lines are always perpendicular to equipotential surfaces. Choose the most appropriate answer:

An electron moves under the field of a charged infinite plane sheet S (surface density +σ). At t = 0 it is 1 m from S with speed 1 m/s. The maximum σ if the electron strikes S at t = 1 s is α [mε₀/e] C/m². Find α.

Two charges of 5Q and −2Q are situated at the points (3a, 0) and (−5a, 0) respectively. The electric flux through a sphere of radius '4a' having center at origin is:

An electric field is given by (6î + 5ĵ + 3k̂) N/C. The electric flux through a surface area 30î m² lying in YZ-plane (in SI unit) is in

The electrostatic potential due to an electric dipole at a distance 'r' varies as

Two identical charged spheres hang by equal strings, making 37° with each other. In a liquid of density 0.7 g/cm³ the angle stays the same. If the sphere material density is 16 g/cm³, the dielectric constant of the liquid is:

A particle of charge '−q' and mass 'm' moves in a circle of radius 'r' around an infinitely long line charge of linear density '+λ'. Then time period will be given as: (Consider k as Coulomb's constant)

Two charges q and 3q are separated by a distance 'r' in air. At a distance x from charge q, the resultant electric field is zero. The value of x is:

Force between two point charges q₁ and q₂ placed in vacuum at 'r' cm apart is F. Force between them when placed in a medium having dielectric K = 5 at 'r/5' cm apart will be:

Two identical charged spheres hang by equal strings, making angle θ with each other. In water the angle stays the same. If the sphere material density is 1.5 g/cc, the dielectric constant of water is (water density = 1 g/cc):

A charged wall gives a uniform field of 2 × 10⁴ N/C. A 2 g particle hangs by a 20 cm silk thread and stays 10 cm from the wall. Its charge is 1/√x μC, where x = [g = 10 m/s²]

C₁ and C₂ are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in figure. The ratio of electric flux passing through C₁ and C₂ is:

A plane sheet of charge density +σ_s lies on the x-y plane. A line charge of density +λ_e lies at z = 4 m, parallel to the y-axis. The field magnitude ratio at (0, 0, 2) to (0, 0, 4) is π√n : 1. Find n (|σ_s| = 2|λ_e|).

An infinitely long positively charged thread has linear charge density λ Cm^-1. An electron revolves in a circular path around the wire. The graph showing how the magnitude of the electron acceleration varies with r will be:

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is xσ/ε₀. The value of x is: (All quantities are measured in SI units)

σ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is:

An electric field E⃗ = (2î + 6ĵ + 8k̂)/√6 passes through the surface of 4 m² area having unit vector n̂ = (2î + ĵ + k̂)/√6. The electric flux for that surface is _______ Vm.

A charge Q at P lies on the axis of dipole 1 at distance r, and on the equatorial plane of dipole 2 at distance r. Both dipoles have opposite charges q separated by 2a. For Q to feel no net force, which statement is correct?

Two point charges −4 μc and 4 μc, constituting an electric dipole, are placed at (−9,0,0) cm and (9,0,0) cm in a uniform electric field of strength 10⁴ NC^-1. The work done on the dipole in rotating it from the equilibrium through 180° is:

Two charges 7 μC and −4 μC are placed at (−7 cm,0,0) and (7 cm,0,0) respectively. Given, ε0 = 8.85 × 10^−12 C² N^−1 m^−2, the electrostatic potential energy of the charge system is:

A square loop of sides a = 1 m is held normally in front of a point charge q = 1 C. The flux of the electric field through the shaded region is (5/p) × (1/ε0) Nm²/C, where the value of p is ________.

Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is the electric field and ε0 is the permittivity of free space between the plates, then potential energy stored in the capacitor is

A small uncharged conducting sphere is placed in contact with an identical sphere but having 4 × 10^−8 C charge and then removed to a distance such that the force of repulsion between them is 9 × 10^−3 N. The distance between them is: (Take (1/(4π ε0)) as 9 × 10⁹ in SI units)

Four identical charges q0 sit at the corners A, B, C, D of a square of side a (configuration 1), then move to the midpoints G, E, H, F (configuration 2). If K = U1/U2 for the two potential energies, K is:

A particle (m, q) is tied to a massless string of length l, fixed at O, in a uniform field E⃗ along the x-axis. End A is displaced 60° from vertical and released from rest. Its speed at the vertical position is:

Three infinitely long wires with linear charge density λ are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?

An electric dipole of dipole moment 6 × 10^−6 Cm is placed in a uniform electric field of magnitude 10⁶ V/m. Initially the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J.

Match List-I with List-II. List-I: (A) field inside a charged spherical shell, (B) field at distance r from an infinite plane sheet, (C) field outside a charged spherical shell, (D) field between oppositely charged plates. List-II: (I) σ/ε0, (II) σ/(2ε0), (III) 0, (IV) σR²/(ε0r²). Choose the correct match:

An electric dipole of mass m, charge q, and length l is placed in a uniform electric field E⃗ = E0 î. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

A point charge causes an electric flux of −2 × 10⁴ Nm² C^−1 to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given ε0 = 8.85 × 10^−12 C² N^−1 m^−2)

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density σ_o. Choose the correct option from the following.

Consider two infinitely large plane parallel conducting plates as shown below: The plates are uniformly charged with a surface charge density +σ and −2σ. The force experienced by a point charge +q placed at the mid point between two plates will be:

A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0,0) in Cartesian coordinate system. The point in between them where the electric field vanishes is:

A small bob (100 mg, +10 μC) hangs by a 1 m insulating string near an infinitely long non-conducting sheet of charge density σ. At equilibrium the string makes 45° with the sheet. Find σ (ε0 = 8.85 × 10^-12 F/m, g = 10 m/s²).

Consider a circular loop that is uniformly charged and has a radius a√2. Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy plane at the origin:

Assertion A: the net dipole moment of a polar, linear isotropic dielectric is not zero even without an electric field. Reason R: without an external field, the permanent dipoles of a polar dielectric point in random directions. Choose the most appropriate answer:

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V. The potential difference between the points A and B (shown in the figure) is:

The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell respectively, are:

Two 10 g balls (−2 μC, 2 μC) sit at the ends of a 20 cm light rigid rod. The rod lies near an infinite sheet (100 μC/m²) at 30° to the sheet. The net torque on the rod is (ε0 = 8.85 × 10^-12):

Two infinite identical charged sheets and a charged spherical body of charge density 'ρ' are arranged as shown in figure. Then the correct relation between the electrical fields at A,B,C and D points is:

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB at 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC?

Two charges q1 and q2 are 30 cm apart. A third charge q3 at C moves along a circular path of radius 40 cm from C to D. The potential energy change for q3 from C to D is (q3K)/(4πε0). Find K:

The electric field in a region is given by E⃗ = (2 î + 4 ĵ + 6 k̂) × 10³ N/C. The flux of the field through a rectangular surface parallel to the x-z plane is 6.0 Nm² C^−1. The surface has area ________ cm².

A dipole (two charges of 2 μC, separation 0.5 μm) sits between capacitor plates (separation 0.5 mm) with its axis parallel to the field from a 5 V potential difference. Rotated 30° from the axis, it feels a realigning torque. The torque value is:

Assertion A: an aircraft outer body is metal, which protects people inside from lightning strikes. Reason R: the electric field inside a cavity enclosed by a conductor is zero. Choose the most appropriate answer:

Electric charge is transferred to an irregular metallic disk as shown in figure. If σ1, σ2, σ3 and σ4 are charge densities at given points, then, choose the correct answer from the options given below:

Two metal spheres of radius R and 3R have same surface charge density σ. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ1 and σ2, respectively. The ratio σ1/σ2 is

An infinitely long wire has uniform linear charge density λ = 2 nC/m. The net flux through a Gaussian cube of side length √3 cm, if the wire passes through any two corners of the cube, would be x Nm² C^−1, where x is: [Neglect any numerical error in calculation and take (1/(4π ε0)) = 9 × 10⁹ SI units]

A point charge of 10^-8 C is placed at origin. The work done in moving a point charge 2 μC from point A(4, 4, 2) m to B(2, 2, 1) m is ____ J. (1/(4π ε0) = 9 × 10⁹ SI Units)

Two identical metallic spheres (radius R, charge Q, mass m) start 4R apart, each moving toward the other at speed u. The minimum u so they just touch each other is (k = 1/(4πε₀), kQ² > Gm²):

Electric field in a region is given by E⃗ = Ax î + By ĵ, where A = 10 V/m² and B = 5 V/m². If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is ____ V.

Six point charges are kept 60° 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 ____. (ε0 is permittivity of free space)

A pendulum bob (mass m, charge q) hangs on a negligible-mass string. A uniform horizontal field E⃗ is applied, changing the tension. Final tension T at the mean position is 3 times initial tension T0. At equilibrium, the string-vertical angle is ____°.

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 bubble is:

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 E⃗ at the center O of the pentagon due to the charges are:

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:

Two charges 7 μC and −2 μC are placed at (900 cm, 0) and (−900 cm, 0) respectively in an external field E = (A/r²) r̂, where A = 9 × 10⁵ N/C·m². Considering the potential at infinity to be zero, the electrostatic energy is ____ J.

Two short dipoles A, B, A having charges ±2 μC and length 1 cm, and B having charges ±4 μC and length 1 cm, are placed with their centres 80 cm apart as shown in the figure. The ratio of the electric field at the centre of A and centre of B 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 q1, q2 and q3 respectively. The potential at a distance r (r < a) from centre is:

The electrostatic potential in a charged spherical region of radius R varies as V = ar³ + b, where a and b are constants. The total charge in the sphere of unit radius is α × π a ε0. The value of α is ____. (Permittivity of free space is ε0)

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

A point charge q = 1 μC is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge q = 24 μC distributed uniformly along its length, as shown in figure. Then the electric force on charge q = 1 μC is ____ N. (Take 1/(4π ε0) = 9 × 10⁹ SI Units)

Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is ____ J.

Which statements are correct: (A) Electrostatic field lines form closed loops. (B) Field lines point radially outward for positive charge. (C) Gauss law holds only for inverse square law force. (D) Field lines cross each other. (E) If a charge is enclosed, all field lines exit the surface.

The electric potential as a function of x, y is given by V = 5(x² − y²) V. The electric field at a point (2, 3) m is ____ V/m.

Two short electric dipoles A and B having dipole moment p1 and p2 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° with the line joining points O and x. The ratio of the dipole moments p2/p1 is ____.

Two charged conducting spheres S1 and S2 of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on S1 and S2 spheres are E_S1 and E_S2 respectively. The value of E_S1/E_S2 is ____.

Two point charges 8 μC and −2 μC are located at x = 2 cm and x = 4 cm, respectively on the x axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is ____.

Two plates A and B lie horizontally, (12/π) cm apart, A on top. Charged oil droplets (1.5 g/cm³, 1 mm radius) are sprayed horizontally at 10 m/s between them. With 300 V across the plates, the droplet acceleration is ____ m/s² (g = 10 m/s²).

Assertion A: in electrostatics, a conductor stores no net charge inside. Reason R: inside a capacitor (no dielectric), free charge carriers placed between the plates feel a force and drift. Choose the correct answer:

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field E1 = E0 x̂. If another electric field E2 = 2E0(ŷ + ẑ) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

A three coulomb charge moves from the point (0, −2, −5) to the point (5, 1, 2) in an electric field expressed as E⃗ = 2x î + 3y² ĵ + 4 k̂ N/C. The work done in moving the charge is ____ J.

A thin half ring of radius 35 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 V/m, then the value of Q is ____ C. (Take 1/(4π ε0) = 9 × 10⁹ SI Units)

Two point charges q1 = 3 μC and q2 = −4 μC are placed at points (2î + 3ĵ + 3k̂) and (î + ĵ + k̂) respectively. Force on charge q2 is ____ N. (Take 1/(4π ε0) = 9 × 10⁹ SI Units)