470
11 Electrostatics
11.33 If the electric potential is given by ϕ = cxy, calculate the electric field.
11.34 Charges Q and −2Q are placed at a fixed distance of separation. Show that
the locus of points in the plane of charges, where the potential is zero, will
be a circle.
[Indian Administrative Services]
11.35 Two identical thin rings, each of radius R, are coaxially placed a distance R
apart. If Q 1 and Q 2 are, respectively, the charges uniformly spread on the
two rings, find the work done in moving a charge q from the centre of one
ring to that of the other.
[Indian Institute of Technology 1992]
11.36 A thin rod of length 2a is placed along the y-axis in the xy-plane. The rod
carries a charge density λ (Fig. 11.5). The point P 1 is located at (0, 2a) and
P 2 at (x, 0).
(a) Find x if the potentials at P 1 and P 2 are equal.
(b) Find the corresponding potential.
Fig. 11.5
11.37 Three charges +q, +q and Q are located at the vertices of a right-angled
isosceles triangle, Fig. 11.6. If the total interaction energy is zero what should
be the value of Q?
Fig. 11.6
11.38 Four charges each of magnitude q are located at the four corners of a square
of side a such that like charges occupy the corners across the diagonals
(Fig. 11.7). Calculate the work done in assembling these charges.
11 Electrostatics
11.33 If the electric potential is given by ϕ = cxy, calculate the electric field.
11.34 Charges Q and −2Q are placed at a fixed distance of separation. Show that
the locus of points in the plane of charges, where the potential is zero, will
be a circle.
[Indian Administrative Services]
11.35 Two identical thin rings, each of radius R, are coaxially placed a distance R
apart. If Q 1 and Q 2 are, respectively, the charges uniformly spread on the
two rings, find the work done in moving a charge q from the centre of one
ring to that of the other.
[Indian Institute of Technology 1992]
11.36 A thin rod of length 2a is placed along the y-axis in the xy-plane. The rod
carries a charge density λ (Fig. 11.5). The point P 1 is located at (0, 2a) and
P 2 at (x, 0).
(a) Find x if the potentials at P 1 and P 2 are equal.
(b) Find the corresponding potential.
Fig. 11.5
11.37 Three charges +q, +q and Q are located at the vertices of a right-angled
isosceles triangle, Fig. 11.6. If the total interaction energy is zero what should
be the value of Q?
Fig. 11.6
11.38 Four charges each of magnitude q are located at the four corners of a square
of side a such that like charges occupy the corners across the diagonals
(Fig. 11.7). Calculate the work done in assembling these charges.