The figure shows some equipotential lines distributed in space. A charged object is moved from point \(A\) to point \(B\).

Choose the correct option:

1. The work done in Fig. (i) is the greatest.
2. The work done in Fig. (ii) is the least.
3. The work done is the same in Fig. (i), Fig. (ii) and Fig. (iii).
4. The work done in Fig. (iii) is greater than Fig. (ii) but equal to that in Fig. (i). 

Subtopic:  Equipotential Surfaces |
 90%
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Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately:
1. spheres
2. planes
3. paraboloids
4. ellipsoids

Subtopic:  Equipotential Surfaces |
 63%
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 A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness \(d_1\) and dielectric constant \(K_1\) and the other has thickness \(d_2\) and dielectric constant \(K_2,\) as shown in the figure. This arrangement can be thought as a dielectric slab of thickness \(d=(d_1+d_2),\) and effective dielectric constant \(K.\) The value of \(K\) is:
        

1. \(\dfrac{K_1d_1+K_2d_2}{d_1+d_2}\) 2. \(\dfrac{K_1d_1+K_2d_2}{K_1+K_2}\)
3. \(\dfrac{K_1K_2(d_1+d_2)}{K_1d_2+K_2d_1}\) 4. \(\dfrac{2K_1K_2}{K_1+K_2}\)
Subtopic:  Dielectrics in Capacitors |
 67%
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Consider a uniform electric field in the \(z\text-\)direction. The potential is a constant:

(a) in all space.
(b) for any \(x\) for a given \( z.\)
(c) for any \( y\) for a given \( z.\)
(d) on the \({x\text-y}\) plane for a given \( z.\)

 
Choose the correct from the given options:

1. (c) and (d) only 2. (a) and (c) only
3. (b), (c) and (d) only 4. (a) and (b) only
Subtopic:  Relation between Field & Potential |
 85%
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Equipotential surfaces:
(a) are closer in regions of large electric fields compared to regions of lower electric fields.
(b) will be more crowded near sharp edges of a conductor.
(c) will be more crowded near regions of large charge densities.
(d) will always be equally spaced.

Choose the correct option:

1. (a), (b) 2. (c), (d)
3. (a), (b), (c) 4. (a), (b), (c), (d)
Subtopic:  Equipotential Surfaces |
 59%
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The work done to move a charge along an equipotential from \(A\) to point \(B:\)
1. cannot be defined as \(-\int_A^B E.dl\)
2. must be defined as \(-\int_A^BE.dl\)
3. is zero
4. can have a non-zero value

Subtopic:  Equipotential Surfaces |
 87%
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In a region of constant potential:

(a) the electric field is uniform.
(b) the electric field is zero.
(c) there can be no charge inside the region.
(d) the electric field shall necessarily change if a charge is placed outside the region.

Choose the correct option:

1. (b), (c) 2. (a), (c)
3. (b), (d) 4. (c), (d)
Subtopic:  Equipotential Surfaces |
 58%
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In the circuit shown in the figure initially, key \(K_1\) is closed and key \(K_2\) is open. Then \(K_1\) is opened and \(K_2\) is closed (order is important).
(Take \(Q_1\) and \(Q_2\) as charges on \(C_1\) and \(C_2\) and \(V_1\) and \(V_2\) as voltage respectively.)

                                     

Then,
(a) charge on \(C_1\) gets redistributed such that \(V_1 =V_2\)
(b) charge on \(C_1\) gets redistributed such that \(Q'_1= Q'_2\)
(c) charge on \(C_1\) gets redistributed such that \(C_1V_1+C_2V_2= C_1E\)
(d) charge on \(C_1\) gets redistributed such that \(Q'_1+Q'_2=Q\)

Choose the correct option:
1. (a), (d)
2. (a), (b), (c)
3. (b), (d)
4. (a), (b), (c), (d)

Subtopic:  Combination of Capacitors |
 51%
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If a conductor has a potential \(V\neq 0\)  and there are no charges anywhere else outside, then:

(a) there must be charges on the surface or inside itself
(b) there cannot be any charge in the body of the conductor
(c) there must be charges only on the surface
(d) there must be charges inside the surface

Choose the correct option:
1. (a), (d)
2. (a), (b), (c)
3. (a), (b)
4. (a), (b), (c), (d)

Subtopic:  Electrostatic Shielding |
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A parallel plate capacitor is connected to a battery as shown in the figure. Consider two situations.

                                          

A: Key \(K\) is kept closed and plates of capacitors are moved apart using insulating handle.
B: Key \(K\) is opened and plates of capacitors are moved apart using the insulating handle.

Then:

(a) In A: \(Q\) remains same but \(C\) changes.
(b) In B: \(V\) remains same but \(C\) changes.
(c) In A: \(V\) remains same and hence \(Q\) changes.
(d) In B: \(Q\) remains same and hence \(V\) changes.
Choose the correct option(s).
1. (a), (b) only
2. (b), (c) only
3. (a), (c), (d) only
4. (c), (d) only
 
Subtopic:  Capacitance |
 67%
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