The work done to move a charge along an equipotential from \(A\) to \(B\):
1. can not be defined as \(-\int_{A}^{B} { \vec E\cdot \vec{dl}}\)
2. must be defined as \(-\int_{A}^{B} {\vec E\cdot \vec{dl}}\)
3. is zero
4. can have a non-zero value.

Subtopic:  Equipotential Surfaces |
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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 statement(s): 

1. (b) and (c) 2. (a) and (c)
3. (b) and (d) 4. (c) and (d)
Subtopic:  Relation between Field & Potential |
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Level 3: 35%-60%
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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 \(C\) gets redistributed such that \(V_1= V_2\)
b. charge on \(C\) gets redistributed such that \(Q_1= Q_2\)
c. charge on \(C\) gets redistributed such that \(C_1V_1+C_2V_2 = C_1 E\)
d. charge on \(C\) gets redistributed such that \(Q_1+Q_2 =Q\)
Choose the correct statement(s)
1. (a) and (c)
2. (a) and (d)
3. (b) and (c)
4. (c) and (d)
Subtopic:  Combination of Capacitors |
Level 3: 35%-60%
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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 the insulating handle.
B: Key \(K\) is opened and plates of capacitors are moved apart using the insulating handle.
Choose the correct option(s):
a. In A, \(Q\) remains the same but \(C\) changes.
b. In B, \(V\) remains the same but \(C\) changes.
c. In A, \(V\) remains the same and hence \(Q\) changes.
d. In B, \(Q\) remains the same and hence \(V\) changes.
1. (a) and (b) 2. (a) and (d)
3. (b) and (c) 4. (c) and (d)
Subtopic:  Capacitance |
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Equipotential 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 |
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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 of as a dielectric slab of thickness \(d= d_1+d_2\) and effective dielectric constant \(K\). The \(K\) is:  

                                  

1. \(\dfrac{{K}_{1} {d}_{1}+{K}_{2} {d}_{2}}{{d}_{1}+{d}_{1}}\) 2. \(\dfrac{{K}_{1} {d}_{1}+{K}_{2} {d}_{2}}{{K}_{1}+{K}_{2}}\)
3. \(\dfrac{{K}_{1} {K}_{2}\left({d}_{1}+{d}_{2}\right)}{{K}_{1} {d}_{2}+{K}_{2} {d}_{1}}\) 4. \(\dfrac{2 {K}_{1} {K}_{2}}{{K}_{1}+{K}_{2}}\)
Subtopic:  Dielectrics in Capacitors |
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Consider a uniform electric field in the \(z\text-\)direction. The potential is 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 \(z\)
 
1. (a), (b), (c) 2. (a), (c), (d)
3. (b), (c), (d) 4. (c), (d)
Subtopic:  Equipotential Surfaces |
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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 the 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 statement(s):
1. (a), (b) and (c) 2. (a), (c) and (d)
3. (b), (c) and (d) 4. (c) and (d)
Subtopic:  Equipotential Surfaces |
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The potential field of an electric field \(E = y\hat i + x\hat j\) is:
1. \(V = -x+y+\) constant
2. \(V\) = constant
3. \(V=-\left({x}^2+{y}^2\right)+\) constant
4. \(V=-x y+\) constant
Subtopic:  Relation between Field & Potential |
Level 3: 35%-60%
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Three capacitors \(A\), \(B\) and \(C\) are connected in a circuit as shown in Fig. What is the charge in \(\mu \text{C}\) on the capacitor \(B\):

    

1. \(\frac{1}{3}\) 2. \(\frac{2}{3}\)
3. \(1\) 4. \(\frac{4}{3}\)
Subtopic:  Combination of Capacitors |
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Level 3: 35%-60%
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