1
IIT-JEE 2008 Paper 2 Offline
+3
-1

Consider a system of three charges $${q \over 3},{q \over 3}$$ and $$- {{2q} \over 3}$$ placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60$$^\circ$$

A
The electric field at point O is $${q \over {8\pi {\varepsilon _0}{R^2}}}$$ directed along the negative x-axis
B
The potential energy of the system is zero
C
The magnitude of the force between the charges at C and B is $${{{q^2}} \over {54\pi {\varepsilon _0}{R^2}}}$$
D
The potential at point O is $${q \over {12\pi {\varepsilon _0}R}}$$
2
IIT-JEE 2008 Paper 2 Offline
+3
-1

A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is $$\frac{d}{3}$$ initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is:

A
$${{6{\varepsilon _0}R} \over {5d + 3Vt}}$$
B
$${{(15d + 9Vt){\varepsilon _0}R} \over {2{d^2} - 3dVt - 9{V^2}{t^2}}}$$
C
$${{6{\varepsilon _0}R} \over {5d - 3Vt}}$$
D
$${{(15d - 9Vt){\varepsilon _0}R} \over {2{d^2} + 3dVt - 9{V^2}{t^2}}}$$
3
IIT-JEE 2008 Paper 2 Offline
+3
-1

STATEMENT 1 : For practical purposes, the earth is used as a reference at zero potential in electrical circuits.

and

STATEMENT 2 : The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by $${Q \over {4\pi {\varepsilon _0}R}}$$

A
Statement 1 is True, Statement 2 is True; Statement 2 is a CORRECT explanation for Statement 1
B
Statement 1 is True, Statement 2 is True; Statement 2 is a NOT CORRECT explanation for Statement 1
C
Statement 1 is True, Statement 2 is False
D
Statement 1 is False, Statement 2 is True
4
IIT-JEE 2008 Paper 2 Offline
+3
-1

The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $$\rho(r)$$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.

The electric field at r = R is :

A
independent of a
B
directly proportional to a
C
directly proportional to a$$^2$$
D
inversely proportional to a
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