Q-1: A field of 103 N/C acts at a point. What will be the force on a charge of 3´10-6C and -2´10-6C, kept there?
The direction of force changes for different charges. For a positive field (due to +ve charge)
1) The force is in direction of field on the +ve charge i.e. repulsive.
2) The force is opposite to field direction on the –ve charge i.e. attractive.
Similar inference can be drawn for negative charges.
Electric field due to:
a) Charged ring of charge Q and radius R.
1) The Center=0.
Linear charge density (l) on ring =
Consider the field at center due to any element =
But the field due to point diametrically opposite = in opposite direction.
\Net field at center = 0 (By symmetry)
2) On the axis =
On axis of ring at distance x.
As obvious from the diagram the field component along the line gets added due to opposite element.
*) By substituting x=0 in 2nd result, we can get the first result.
*) Student should verify that the graph is of the following manner.
b) Due to a straight charged rod of length 2L with charge per unit length ‘’ at a distance ‘a’ on its perpendicular bisector.
The rod is divided into infinitely small elements and the field due to symmetrically; opposite part add up as shown in figure (7).
Net field at P.
1) If x>>a, E = like a point charge.
2) If L
i.e. for infinite length
1) How did the electric field cancel in one direction and add in another?
Observe the direction of electric field of two points which are symmetrically opposite.
Along the axis, net field =
Along the perpendicular,
Net field =
Similarly all fields along the perpendicular to axis cancel out.