Electrostatics
- The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K_1 and K_2 with thickness 3/8d and d/2, respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than wh… Answer: 1. 2.66 Key idea: for slabs inserted in a capacitor, C=ε₀A/d-t₁-t₂+t₁/K₁+t₂/K₂ . Here t₁=3/8d , t₂=1/2d , and C=2C₀ , so the denomin... 1
- Two identical charged conducting spheres A and B have their centres separated by a certain distance. Charge on each sphere is q and the force of repulsion between them is F. A third identical uncharged conducting sphere is brought in contact with sph… Answer: 4. 3F/8 Key idea: identical conducting spheres share charge equally on contact. Third sphere touches A: A and C each have q/2 . Then... 1
- An electric dipole with dipole moment 5×10^-6 Cm is aligned with the direction of a uniform electric field of magnitude 4×10^5 N/C. The dipole is then rotated through an angle of 60^° with respect to the electric field. The change in the potential en… Answer: 2. 1.0 J Key idea: potential energy of a dipole is U=-pEcosθ . Initially θ=0^° and then 60^° : Δ U=pE(cos0^°-cos60^°)=5×10⁻⁶×4×10⁵×1... 1
- If the plates of a parallel plate capacitor connected to a battery are moved close to each other, thenA. 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 rem… Answer: 3. A, C and E only Key idea: The capacitor stays connected to the battery, so the voltage V stays fixed. Moving the plates closer re... 1
- In the following circuit, the equivalent capacitance between terminal A and terminal B is : Answer: 2. 2 μ F Key idea: The circuit is symmetric, so the middle capacitor is part of a balanced bridge and holds no charge. Let M be the... 1
- 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 P of magnitude, 4×10^-6… Answer: 4. A is true but R is false. Key idea: Potential of a dipole at an axial point: V=±p/4πε₀r² . Assertion: V=frac9×10⁹×4×10⁻⁶2²=9×10³... 1
- 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 1/4πε_0=9×10^9 SI units) Answer: 1. zero Key idea: For a charged shell, the potential is the same at every point inside and on the surface: V=kq/R . C is the centre... 1
- An electric dipole is placed as shown in the figure. The electric potential (in 10^2 V) at point P due to the dipole is (ε_0 = permittivity of free space and 1/4πε_0=K): Answer: 2. (3/8)qK P lies on the axis of the dipole. Distances from P: to +q it is 5-3=2 cm, to -q it is 5+3=8 cm. V=Kq(dfrac10.02-dfrac10.0... 1
- The equivalent capacitance of the system shown in the following circuit is : Answer: 2. 2 μ F From the figure, one 3 μ F capacitor is in series with a parallel pair of 3 μ F capacitors. Parallel pair: 3+3=6 μ F. Serie... 1
- An electric dipole is placed at an angle of 30^° with an electric field of intensity 2×10^5 N C^-1. It experiences a torque equal to 4 N m. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm. Answer: 1. 2 mC Torque on a dipole: τ = pEsinθ , with p=q· l . 4 = q(0.02)(2×10⁵)sin30^° = q× 2000 q = 2×10⁻³ C = 2 mC. 1
- If _S E· dS=0 over a surface, then : Answer: 2. the number of flux lines entering the surface must be equal to the number of flux lines leaving it. oint vec E· dvec S = q_enc/ε₀... 1
- 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 : Answer: 3. 1/R³ The two charges form an electric dipole with dipole moment p=qL . Their fields nearly cancel at a large distance. For Rgg L... 1
- A capacitor of capacitance C = 900 pF is charged fully by 100 V battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900 pF as shown in figure (b). The electrostati… Answer: 4. 2.25 × 10⁻⁶ J Initial charge: Q=CV=900×10⁻¹²×100=9×10⁻⁸\ C . After connecting to an identical uncharged capacitor, charge is cons... 1
- The angle between the electric lines of force and the equipotential surface is : Answer: 4. 90° Work done in moving a charge along an equipotential surface is zero, so the field has no component along the surface. Hence e... 1
- Two hollow conducting spheres of radii R_1 and R_2 (R_1 >> R_2) have equal charges. The potential would be : Answer: 3. more on smaller sphere For a conducting sphere the potential is V=kQ/R , depending only on charge and radius, not on the material... 1
- Polar molecules are the molecules : Answer: 4. having a permanent electric dipole moment. Polar molecules (such as H₂O , HCl) have centres of positive and negative charge that... 1
- Two charged spherical conductors of radius R_1 and R_2 are connected by a wire. Then the ratio of surface charge densities of the spheres (σ_1/σ_2) is : Answer: 2. R₂/R₁ Key idea: connected conductors are at the same potential. V=kQ/R=kσ4π R²/R=4π kσ R . Equal V gives σ₁R₁=σ₂R₂ , so σ₁/σ₂=R₂/... 1
- 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. Answer: 4. 1980 V Key idea: total charge and volume are conserved when drops merge. Volume: 4/3π R³=27·4/3π r³⇒ R=3r . Charge: Q=27q . V_big... 1
- The equivalent capacitance of the combination shown in the figure is : Answer: 2. 2C Key idea: wires joining the two sides short-circuit a capacitor, and the rest become parallel. The right-hand vertical wire jo... 1
- A dipole is placed in an electric field as shown. In which direction will it move ? Answer: 2. towards the right as its potential energy will decrease. Key idea: in a non-uniform field a dipole feels a net force towards the... 1
- A parallel plate capacitor has a uniform electric field 'E' 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 : (ε_0 = permittivity of free space) Answer: 3. 1/2ε₀E²Ad Key idea: energy density in an electric field is 1/2ε₀E² ; multiply by the volume between the plates. U=1/2ε₀E²× Ad . O... 1
- The capacitance of a parallel plate capacitor with air as medium is 6 μF. With the introduction of a dielectric medium, the capacitance becomes 30 μF. The permittivity of the medium is :(ε_0 = 8.85×10^-12 C^2 N^-1 m^-2) Answer: 3. 0.44×10⁻¹⁰ C ² N ⁻¹ m ⁻² Capacitance with a dielectric of relative permittivity K is C=KC₀ . So K=30/6=5 Permittivity of the medi... 1
- A short electric dipole has a dipole moment of 16×10^-9 C m. 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^° with the dipole axis is :≤ft(1/4πε_0 = 9… Answer: 2. 200 V Potential of a short dipole: V=1/4πε₀pcosθ/r² . V=frac9×10⁹×16×10⁻⁹×cos60^°(0.6)²=144×0.5/0.36=200\ V Answer: option 2. 1
- 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 15 cm from the centre of the sphere ?≤ft(1/4πε_0 = 9×10^9\ N m^2/C^2) Answer: 2. 1.28×10⁵ N/C Outside a uniformly charged sphere, the field is the same as that of a point charge at the centre. E=1/4πε₀Q/r²=frac... 1