8. An electric dipole of moment p⃗ is placed in a uniform electric field E⃗. Then (i) the torque on the dipole is p⃗ ×E→ (ii) the potential energy of the system is p⃗ .E→ (iii) the resultant force on the dipole is zero. Choose the correct option. (a) (i), (ii) and (iii) are correct (b) (i) and (iii) are correct and (ii) is wrong (c) only (i) is correct (d) (i) and (ii) are correct and (iii) is wrong

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants