^Dimensionless Variables
^Dimensionless Variables
Are the physical quantities which have no dimensions but have variable values.
e.g. Angle, Strain, Specific gravity etc.
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^Field due to charged conductors
Field due to charged conductors
Under electrostatic conditions for a conductor of any shape,
^Point charge
Point charge
A body of almost no size is called a point body or discrete body i.e. a sphere of radius R → 0 is a point like body. Both field & potential are not defined on a discrete charge, as r → 0 implies E & V → ∞. Outside the point charge field & potential are
Field of a point charge has following properties
1. radially outward if charge is positive & inwards if it is negative.
2. at finite distance around it, field is spherically symmetric & obeys inverse square law i.e. it is not uniform
3. at infinite distance from the it, field is zero
4. maxi. it the charge is placed in vacuum or air.
^Factors deciding flux
Factors deciding flux
Electric flux depends only upon
(a) the number of charges enclosed by Gaussian surface
(b) nature of charges enclosed by Gaussian surface
(c) nature of the medium. & is independent of
(d) size of surface
(e) distance between charges inside the surface
(f) distribution of charges.
Diagram explains that the net electric flux through each surface is the same irrespective of the shapes of the closed surfaces surrounding a charge q.
Diagram explains that the no net flux is linked with the closed surface if a point charge is located outside a closed surface as in this case the number of lines entering the surface equals the number leaving the surface.
Diagram explains that the net electric flux through any closed surface depends only on the charge inside that surface. The net flux through surface SA is q1/e0, the net flux through surface SB is 
and net flux through surface SC is zero.
*Value in S.I units
*Value in S.I units
^Numerical & unit
^Numerical & unit
The magnitude of a quantity doesn’t change with the change of unit. i.e. numerical & unit of a physical quantity are inversely proportional.
^For uniformly charged semi ring
For uniformly charged semi ring
For a ring α & Β → 900 & E becomes
^Uniformly charged ring of radius R
Uniformly charged ring of radius R
1. Charge on a circular ring of radius R & uniform linear charge density λ is, Q = λ 2 πR
2. Electric field on axis at P, 
3. Electric field at centre C = 0
4. 
5. Variation of elec. field vector with distance
6. 
7. 
^Electric dipole
Electric dipole
1. On axial line: 
2. On eq. line: 
3. At center: 
4. Following diagram shows variation of electric field with distance on axial line of dipole.
5. 
6. For short dipole
(a) On axial line: 
(b) On equatorial line: 
(c) Any point: 
directed at 
with Ex.
(d) 
^Potential energy of point charges
Potential energy of point charges
1. For a system of two point charges 
2. For a system of three point charges
3. 
4. For a stable system U is minimum, its first derivative w.r.t. position (= – F) is zero & its second derivative w.r.t. position is +ve.
