Electrostatics
- In a certain region of space with volume 0.2 m^3, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is : Answer: 1. zero Electric field is the negative gradient of potential: E=-dV/dx . The potential is constant (5 V) throughout the region, so i... 1
- Two point charges A and B, having charges +Q and -Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes : Answer: 2. 9F/16 25% of A's charge is 0.25Q . After transfer: q_A=0.75Q and q_B=-Q+0.25Q=-0.75Q . Coulomb force F∝ q_Aq_B at the same distan... 1
- Two parallel infinite line charges with linear charge densities +λ C/m and -λ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges ? Answer: 3. λ/πε₀ R N/C The field of an infinite line charge at distance r is E=λ/2πε₀r . Midway, r=R for each line. The + λ line pushes away... 1
- A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre : Answer: 2. zero as r increases for r < R, decreases as r increases for r > R For a uniformly charged hollow sphere, by Gauss's law: Inside (... 1
- The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is Answer: 1. independent of the distance between the plates. The field of one plate is σ/2ε₀ , and this acts on the charge Q of the other plat... 1
- 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 throu… Answer: 1. smaller The force magnitude is eE for both particles, so a=eE/m . Fall distance h=1/2at² gives t=√(2h/a) . The electron has a muc... 1
- Suppose the charge of a proton and an electron differ slightly. One of them is -e, the other is (e+Δ e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart… Answer: 2. 10⁻³⁷ C Key idea: each hydrogen atom then has a net charge Δ e , and the electric repulsion balances gravity. (Δ e)²/4πε₀d²=Gm_h²... 1
- The diagrams below show regions of equipotentials.A positive charge is moved from A to B in each diagram. Answer: 1. In all the four cases the work done is the same. Key idea: work done by an external agent moving a charge slowly is W=q(V_B-V_A)... 1
- 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 : Answer: 1. decreases by a factor of 2 Key idea: charge is conserved when the second capacitor is connected, but energy is not. Initially U=Q... 1
- A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k_1,k_2,k_3 and k_4 as shown in the figure below. If a single dielectric material is to be used to have th… Answer: 2. 2/k=3/k₁+k₂+k₃+1/k₄ The upper half (thickness d/2 ) has three dielectrics side by side, each of area A/3 , so they are in paralle... 1
- An electric dipole is placed at an angle of 30° with an electric field intensity 2×10^5 N/C. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is Answer: 1. 2 mC Torque on a dipole: τ=pEsinθ , with p=q l . 4=q(0.02)(2×10⁵)sin30^°=q×2000 q=4/2000=2×10⁻³ C =2 mC. Option (1). 1
- Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (d << l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a… Answer: 3. v ∝ x^(-1/2) Key idea: at equilibrium, the electric force balances the horizontal component of tension. With tanθ≈x/2l : kq²/x²=m... 1
- A capacitor of 2\ μ F is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is : Answer: 4. 80% Key idea: charge is conserved; it is shared between the capacitors until the potentials are equal, and the difference in ener... 1