Charges `Q_1 and Q_2` lie inside and outside, respectively, of a closed surface S. Let E be the field at any point on S and `phi` be the flux of E over S.

P i sa point on an equipotential surface S . The field at P is E .

Electric flux through a closed surface in free space enclosing a charge q is

A conducting sphere S_(1) intersects a closed surface S_(2) as shown in the figure.A positive charge q is placed at a point P .What is the value of electric flux through the surface S_(2) ? q P

Three point charges are placed as shown in the figure. S is a gaussian surface phi is the net flux passing through surface A and E be the electric field at point P on the surface, then

Let E1 and E2, be two ellipses whose centers are at the origin.The major axes of E1 and E2, lie along the x-axis and the y-axis, respectively. Let S be the circle x^2 + (y-1)^2= 2. The straight line x+ y =3 touches the curves S, E1 and E2 at P,Q and R, respectively. Suppose that PQ=PR=[2sqrt2]/3.If e1 and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is(are):

Let E1 and E2, be two ellipses whose centers are at the origin.The major axes of E1 and E2, lie along the x-axis and the y-axis, respectively. Let S be the circle x^2 + (y-1)^2= 2. The straight line x+ y =3 touches the curves S, E1 and E2 at P,Q and R, respectively. Suppose that PQ=PR=[2sqrt2]/3.If e1 and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is(are):

S_1 and S_2 are two hollow concentric spheres enclosing charges Q and 2Q , respectively, as shown in figure. i. What is the ratio of the electric flux through S_1 and S_2 ? ii. How will the electric flux through sphere S_1 change if a medium of dielectric constant 5 is introduced in the space inside S_1 in place of air. .

Consider two charged metallic spheres S_1 and S_2 of radii R and 4R, respectively. The electric fields E_1 (on S_1 ) and E_2 (on S_2 ) on their surfaces are such that E_1/E_2 = 5/1 . Then the ratio V_1 (on S_1 ) / V_1 (on S_2 ) of the electrostatic potentials on each sphere is :