EF from uniformly charged solid sphere of radius R r R E 1 4 Q R 2 r R E 1 4 Q

# Ef from uniformly charged solid sphere of radius r r

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EF from uniformly charged solid sphere of radius R: r > R E = 1 4 ⇡✏ 0 Q R 2 r < R E = 1 4 ⇡✏ 0 Q R 3 r Electrical Potential of single charge: V = kQ r Electric potential energy of system: U = kq 1 q 2 r = QV 2 = CV 2 2 = Q 2 2 C Converting electric potential to electric potential energy: U = qV Work done in moving charge from A to B: Δ V = V B - V A Potential from dipole: V = kP r 2 Potential on axis of disk: V = 2 k σ | x | ( q 1 + R 2 z 2 - 1) Potential at distance R from point charge and sheet of charge: V = - 2 k σ | x | + kq ( 1 r - 1 a ) Relationship between E and V: E = -r V Torque exerted by field on dipole: = pEsin ( ) EF between 2 curved rods: 4 kq r 2 Charge between 2 concentric spheres: Q B = q o - ( q A - q i ) - q i Gauss’ Law for a cylinder: 2 E rL = q 0 where q = p ( r 2 o - r 2 i ) L EF from infinitely long cylindrical wire: Outside: E = σ r 0 x Geometrical Formulas Sphere Surface Area: 4 r 2 Volume: 4 3 r 3 Cylinder Surface Area: 2 r 2 + 2 rh Volume: r 2 h Cube Surface Area: 6 a 2 Volume: s 3 Tips On changing capacitance: Capacitance changed while connected, charge changes. Capacitance changed while disconnected, voltage changes. If reconnected, voltage readjusts and energy will change.

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Important Notes: Electric field lines point away (+) and towards (-). Strength of field is indicated by the density of lines. Charge on conductor is only on surface, not inside. Field due to dipole is proportional to the mag. Of the dipole moment and decreases with the cube of distance. Dipole has no net force, but has net torque. E-field outside conductor Line of charge Discontinuity Conducting sphere insulating sphere Axis of charged ring Axis of charged disk Infinite plate Dipole moment Torque on dipole Potential energy of dipole

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