ELECTRIC CHARGES AND FIELDS
Q.1 A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its
volume as shown in the figure. Is the electric field exist inside the emptied space of the sphere? (2 marks)
1. Let us consider a uniformly charged solid sphere without any cavity. Let the charge per unit volume be
s and O be the centre of the sphere. Now consider a uniformly charged sphere of negative charged
density s having its centre at O′. Also let OO′ be equal to a.
Let us consider an arbitary point P in the small sphere. The electric field due to charge on big sphere
E1 = OP .
Also the electric field due to small shpere E 2 = PO' O
\ The total electric field E 2 = E 1 + E2 = éOP + PO'ù = O'
3e0 ë û 3e OO'
This will have a finite value which will be uniform.
Q.2 Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. What is the
net charge on the sphere positive, negative or zero? (2 marks)
2. When a positive point charge is placed outside a conducting sphere, a rearrangement of charge takes
place on the surface. But the total charge on the sphere is zero as no charge has left or entered the sphere.
net charge = 0
+q – +
Q.3 If you place a free electron and a free proton in the same electric field, how will the forces acting on them
compare? How will their accelerations compare ? Their directions of travel? (2 marks)
3. When we place a free electron and a free proton in the same electric field, the same amount of force will act
on both of them as both have equal amount of charge. But the forces on both of them will be in opposite
The acceleration of electron will be more than the acceleration of proton as electron has less mass than
that of proton.
Electron has negative charge, therefore, it will travel in a direction opposite to the electric field. But proton,
having positive charge, will travel in the direction of the electric field.
2 Science and Technology Workbook for Class X
Q.4 Two uniformly charged large plane sheets S 1 and S 2 having charge densities σ1 and σ2 (σ1 > σ2 ) are
placed at a distance d parallel to each other. A charge q 0 is moved along a line of length a(a < d) at an
angle 45º with the normal to S 1 . Calculate the work done by the electric field. (2 marks)
σ1 σ S1 S2
4. E1 = E2 = 2
ε0 ; ε0
σ − σ2 σ1
E = E1 − E2 = 1 E
W = q0 E × a
q (σ − σ2 )a
∴ W= 0 1
Q.5 Electric field on the axis of a small electric dipole at a distance r is E1 and E 2 at a distance 2r on the
equatorial line. How are E1 and E 2 related to each other? (2 marks)
5. Electric field on the axial line of a short dipole.
E1 = K (along P )
Electric field on the equatorial line of a short dipole.
E2 = K (opposite to P )
−K P − KP −K2P
= = =
(2r) 3 8r3
∴ E2 =