Question 1 :
The effective capacitance between the points <em>x</em> and <em>y</em> in the will be <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c2e91da6d070c2abf990"/>

Question 2 :
A parallel plate capacitor is made of two circular plates separated by a distance {tex}5\, \mathrm { mm } {/tex} and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is {tex} 3 \times 10 ^ { 4 } \mathrm { V } / \mathrm { m } {/tex} the charge density of the positive plate will be close to:

Question 3 :
A half ring of radius <em>R</em> has a charge of λ per unit length. The potential at the center of the half ring is

Question 4 :
Half part of ring is uniformly positively charged and other half is uniformly negatively charged. Ring is in equilibrium in uniform electric field as shown and free to rotate about an axis passing through its centre and perpendicular to plane. The equilibrium is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c33df1a5a149feab9a64"/>

Question 5 :
If an insulated non-conducting sphere of radius <em>R</em> has charge density ρ. The electric field at a distance <em>r</em> from the centre of sphere (<em>r</em> < <em>R</em>) will be

Question 6 :
A non-conducting ring of radius <em>R</em> has charge <em>Q</em> distributed uniformly over it. If it rotates with an angular velocity ω, the equivalent current will be

Question 7 :
The equivalent capacity of the combination shown in figure is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c2e4bfef6349df00fe60"/>

Question 8 :
If each capacitor has capacitance <em>C</em> then find <em>C_AB</em> <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c32b1da6d070c2abfa18"/>

Question 9 :
A charge <em>q</em> is placed at the midpoint of the line joining two equal charges <em>Q</em>. The system of three charges will be in equilibrium when <em>q</em> has the value

Question 10 :
A charge <em>q</em> is placed at the centre of the line joining two equal charges <em>Q</em>. The system of the three charges will be in equilibrium if <em>q</em> is equal to

Question 11 :
Two infinitely long parallel conducting plates having surface charge densities +<font face="Symbol">&Sigma;</font> and –<font face="Symbol">&Sigma;</font> respectively, are separated by a small distance. The medium between the plates is vacuum. If ε₀ is the dielectric permittivity of vacuum, then the electric field in the region between the plates is

Question 12 :
Two conducting spheres of radii <em>r</em>₁ and <em>r</em>₂ are at the same potential. The ratio of their charges is

Question 13 :
The charge per unit length for a very long straight wire is λ. The electric field at points near the wire (but outside it) and far from the ends varies with distance <em>r</em> as

Question 14 :
A cylinder of radius <em>R</em> and length <em>L</em> is placed in a uniform electric field <em>E</em> parallel to the axis of cylinder. The total flux through the curved surface of the cylinder is given by

Question 15 :
Two identical charges are placed at the two corners of an equilateral triangle. The potential energy of the system is <em>U</em>. The work done in bringing an identical charge from infinity to the third vertex is

Question 16 :
In the arrangement shown all the plates have equal area <em>A</em> and spacing <em>d</em> between them. The equivalent capacitance between point <em>P</em> and <em>Q</em> will be, <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c33ef1a5a149feab9a65"/>

Question 17 :
Two parallel wires are suspended in vacuum. When the potential difference between the wires is 30 V then the charge on the wires is $140\mu C$. The capacitance of the system of wires will be :<br/>

Question 18 :
<p class="wysiwyg-text-align-left"><span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small">$n$ capacitors each of capacitance 2 $\mu F$ are connected in parallel and a potential difference of $200\; V$ is applied to the combination. The total charge on all the positive plates is $1$ Coulomb then $n$ is equal to :<br/></span></span></p>

Question 19 :
The potential across a $25.0$ microfarad capacitor is $5.0 V$.What is the charge on the capacitor?

Question 20 :
If 'Q' is the quantity of charge, 'V' the potential and 'C' the capacity of a conductor, they are related as:

Question 21 :
The capacitance of a metallic sphere is $1\mu F$, then it's radius is nearly<br>

Question 22 :
The capacitance of spherical conductor of radius r is proportional to :<br/>

Question 23 :
Two spheres of $3 \mu F$ and $5 \mu F$ are charged to a potential of $300V$ and $500V$ respectively The common potential will be :

Question 24 :
If the plates of a parallel plate capacitor are not equal in area, then quantity of charge

Question 25 :
A parallel plate air capacitor has a capacitance of $100\ \mu F$. The plates are at a distance $d$ apart. If a slab of thickness $t(t \le d)$ and dielectric constant $5$ is introduced between the parallel plates, then the capacitance will be <br>

Question 26 :
A dipole of dipole moment <em>p</em> is kept at the centre of a ring of radius <em>R</em> and charge <em>q</em>. The dipole moment has direction along the axis of the ring. The resultant force on the ring due to the dipole is

Question 27 :
Two capacitors of $10\ pF$ and $20\ pF$ are connected to $200\ V$ and $100\ V$ sources respectively. If they are connected in parallel by the wire, what is the common potential of the capacitors?

Question 28 :
A simple pendulum of mass m charged negatively to q coulomb oscillates with a time period T in a downward electric field E such that mg &gt; qE. If the electric field is withdrawn, the new time period :<br/>

Question 29 :
The capacity of a parallel plate condenser is $10\mu F$, when the distance between its plates is $8 $cm. If the distance between the plates is reduced to $4$ cm, then the capacity of this parallel plate condenser will be :<br/>

Question 30 :
Metallic sphere of radius $R$ is charged to potential $V$. then charge $q$ is proportional to:

Question 31 :
Two metal spheres (radii $r_1, r_2$ with $r_1 &lt; r_2$) are very far apart but are connected by a thin wire. If their combined charge is Q, then what is their common potential?

Question 32 :
<span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small"></span></span><p class="wysiwyg-text-align-left">The plates of a parallel plate capacitor are charged to $200\ V$ and then, the charging battery is disconnected. Now, a dielectric slab of dielectric constant $5$ and thickness $4\ mm$ is inserted between the capacitor plates. To maintain the original capacity, the increase in the separation between the plates of the capacitor is:</p>

Question 33 :
A large insulated sphere of radius $r$ charged with $Q$ units of electricity is placed in contact with a small insulated uncharged sphere of radius $r$' and is then separated. The charge on smaller sphere will now be :<br/>

Question 34 :
The capacitance of two concentric spherical shells of radii $R_{1} \, and \, R_{2} (R_{2} &gt; R_{1})$ is:

Question 35 :
Three capacitors of capacitances 6 &#181;F each are available. The minimum and maximum capacitances, which may be obtained are

Question 36 :
The frequency for which $5\mu F$ capacitor has a reactance of $10,000 \Omega$ is

Question 37 :
In 1909, Robert Millikan was the first to find the charge of an electron in his now-famous oil-drop experiment. In that experiment, tiny oil drops were sprayed into a uniform electric field between a horizontal pair of oppositely charged plates.The drops were observed with a magnifying eyepiece, and the electric field was adjusted so that the upward force on some negatively charged oil drops was just sufficient to balance the downward force of gravity. That is, when suspended, upward force qE just equaled mg. Millikan accurately measured the charges on many oil drops and found the values to be whole number multiples of $1.6 \times 10^{-19} C$ the charge of the electron. For this, he won the Nobel prize. If a drop of mass $1.08 \times 10^{-14} kg$ remains stationary in an electric field of $1.68 \times 10^5 NC^{-1}$, then the charge of this drop is :<br/>

Question 38 :
Two plates (area = $5$ ) charged to $ +q_1$ and $+q_2 (q_2 &lt; q_1) $ are brought closer to form a capacitor of capacitance $C$ . The potential difference across the plates is :

Question 39 :
The magnitude of the electric field $E$ in the annular region of a charged cylindrical capacitor:<br/>

Question 40 :
Two spherical conductors $A$ and $B$ or radii $2 mm$ and $3 mm$ are separated by a distance of $5 cm$ and are uniformly charged. If the spheres are connected by a conducting wire, then, in equilibrium position, the ratio of the magnitudes of electric fields at the surface of the spheres $A$ and $B$ is :

Question 41 :
A parallel plate capacitor has plates of unequal area. The larger plate is connected to the positive terminal of the battery and the smaller plate to its negative terminal. Let $Q_+$ and $Q_-$ be the charges appearing on the positive and negative plates respectively.

Question 42 :
The capacity of a spherical condenser is $1\mu F$. If the spacing between the two spheres is $1\ mm$, the radius of the outer sphere is.

Question 43 :
At the moment $t=0$, an electron leaves one plate of a parallel-plate condenser with a negligible velocity. An accelerating voltage varying as $V=at$, where $a$ is a constant is applied between the plates. The separation between the plates is $l$. The velocity of the electron at the moment it reaches the opposite plate will be :<br/>

Question 44 :
A capacitance is formed by two identical metal plates. The plates are given charges $Q_1$ and $Q_2 (Q_2 &lt; Q_1) $ . If capacitance of the capacitor is $C,$ what is the p.d. between the plates?

Question 45 :
Two capacitors of capacitance $C_1$ and $C_2$ respectively are charged to $120 V$ and $200 V$ respectively. It is found that by connecting them together the potential on each one can be made zero. Then :<br/>