Electric potential, potential difference, equipotential surfaces
- 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
- 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
- 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
- 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
- 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