1. Electrostatic potential
1.1. Potential difference
1.1.1. V=V(b)-V(a)=w(ab)/q°
1.1.2. Defined as amount of work done in bringing unit positive charge from one point to other against electrostatic forces
1.1.3. Unit is volt (Alessandro Volta)
1.2. Electric potential
1.2.1. Defined as amount of work done in moving a unit positive charge of 1coulomb from infinity to that point against electrostatic forces
1.2.2. Due to a point charge
1.2.2.1. W=kqq°/r We know- V=w/q°=kq/q
1.2.2.2. Potential due to single charge is spherically symmetric
1.2.2.3. Depends on 1/r
1.2.2.4. Depends only on r
1.2.3. Scalar quantity (direct addition)
1.2.4. Due to a dipole
1.2.4.1. At axis- kp/r^2
1.2.4.2. At equatorial - v=0
1.2.4.3. At any point - v=kpcos(theta)/r^2
1.2.4.4. Potential due to a dipole is cylindrically symmetric
1.2.4.5. Depends on 1/r^2
1.2.4.6. Depends on r and theta
1.2.5. Due to system of charges
1.2.5.1. V=v(1)+v(2)+----------+v(n)
1.2.6. Due to uniformly charged thin sphere
1.2.6.1. Outside - kq/r
1.2.6.2. Inside - kq/R
1.2.6.3. Surface - kq/R
1.3. Relation between electric field and electric potential
1.3.1. E=-dv/dr (potential gradient)
1.3.1.1. Rate of change of potential with distance is called potential gradient
1.3.2. Electric field at any point is equal to the negative of the potential gradient
1.3.3. V=-E.dr
2. Capacitance
2.1. Defined as the charge required to increase the potential of the conductor by unit amount
2.2. Q=CV,C=Q/V
2.3. Depends on size and shape of conductor
2.4. Permittivity
2.5. Presence of other conductors in its neighborhood
2.6. Combination of capacitors
2.6.1. Series
2.6.1.1. Charge on each capacitor is same
2.6.1.2. 1/C(eq)= 1/C(1)+1/C(2)+------+1/C(n)
2.6.2. Parallel
2.6.2.1. Potential difference across each capacitor is same
2.6.2.2. C(eq)=C(1)+C(2)+--------+C(n)
2.7. Unit is farad
2.8. C of isolated spherical conductor C=4π€°R
2.9. Capacitor is a conductor which stores electric charge and electrical energy
2.10. Capacitance of an isolated conductor is small because of breakdown
2.11. Parallel plate capacitor
2.11.1. E=sigma/€°, C=€°A/d
2.11.2. Energy stored U = 1/2cv^2 or 1Q^2/2C= 1/2QV
2.12. Dielectric
2.12.1. Insulating medium
2.12.2. Dielectric constant K = E°\E°-E(polarized)
2.12.3. If dielectric is completely filled C=k€°A/d =kC°
2.12.4. If dielectric is partially filled C=€°A/d-t+t/k
2.12.5. Effect of dielectric
2.12.5.1. Battery disconnected from the capacitor
2.12.5.1.1. Q=Q° charge remains same
2.12.5.1.2. V=V°/k potential decreases k times
2.12.5.1.3. E=E°/k electric field decreases k times
2.12.5.1.4. U=U°/k energy decreases k times
2.12.5.1.5. C=kC° capacitance increases k times
2.12.5.2. Battery connected across the capacitor
2.12.5.2.1. Q=kQ° charge increases k times
2.12.5.2.2. E=E° remains constant
2.12.5.2.3. V=V° remains constant
2.12.5.2.4. U=kU° increases k times
2.12.5.2.5. C=kC° increases k times
3. Equipotential surfaces
3.1. Surface that has same electric potential at every point
3.2. Properties
3.2.1. No work is done in moving a test charge over an equipotential surface
3.2.2. Electric field is always normal to the equipotential surface at every point
3.2.3. No two equipotential surfaces can intersect each other
3.2.4. Equipotential surfaces are close together in the region of strong field and farther apart in the region of weak field
4. Electric potential energy
4.1. Defined as amount of work done in assembling the charges at their locations by bringing them in , from infinity
4.2. U=kq(1)q(2)/r
4.3. Potential energy of a dipole in uniform electric field
4.3.1. U= -pEcos(theta) = -p.E
5. Behaviour of conductors in electric field
5.1. Net electric field is zero inside a conductor
5.2. Potential is constant within and on the surface of a conductor
5.3. Just outside the surface of a charged conductor electric field is normal to the surface
5.4. Electric field is zero in the cavity of a hollow charged conductor
5.5. The net charge in the interior of a conductor is zero and any excess charge resides at its surface
5.6. Electrostatic shielding
5.6.1. Phenomenon of making a region free from any electric field is called electrostatic shielding
5.6.1.1. Faraday cage