Electric Potential at a Point in Space Due to a Point Charge Q

Q. Electric potential is given by V=6x-8xy^2-8y+6yz-4z^2 then electric force acting on a 2 coulomb point charge placed at origin is

Q.

An arc of radius r carries charge. The linear density of charge is $\lambda$ and the arc subtends an angle $\frac{\pi }{3}$ at the centre. What is electric potential at the centre?

1. $\frac{\lambda }{4{ϵ}_0}$
2. $\frac{\lambda }{8{ϵ}_0}$
3. $\frac{\lambda }{12{ϵ}_0}$>
4. $\frac{\lambda }{16{ϵ}_0}$

Q.

Charges of $+\frac{10}{3}\times {10}^{-9}C$ are placed at each of the four corners of a square of side 8 cm.

The potential at the intersection of the diagonals is

1. $150\sqrt{2}$ volt
2. $1500\sqrt{2}$ volt
3. 900 volt
4. $900\sqrt{2}$ volt

Q. A sphere of radius R has a uniform distribution of electric charge in its volume. At a distance x from its centre, for x < R, the electric field is directly proportional to

1. $x$
2. $\frac{1}{x^2}$
3. $\frac{1}{x}$
4. $x^2$

Q. determine electrostatic self energy of a uniformly charged solid sphere

Q.

A charge q is placed at the center of the cube of side l. What is the electric flux passing through two opposite faces of the cube?

Ans. $\frac{1}{3}\frac{q}{{\epsilon }_0}$

Q. An infinite number of charges of equal magnitude q, but of opposite sign are placed alternately starting with positive charge along x- axis at x = 1 m; x = 2 m, x = 4 m, x= 8 m and so on. The electric potential at the point x = 0 due to these charges will be (in S.I units and k = $\frac{1}{4\pi {ϵ}_0}$

1. $\frac{kq}{2}$
2. $\frac{k2q}{3}$
3. $\frac{kq}{3}$
4. $\frac{k3q}{2}$

Q.

The electric flux from a cube of edge $\mathrm{l}$ is $\mathrm{\varphi }$. If an edge of the cube is made $2\mathrm{l}$ and the charge enclosed is halved, its value will be

1. $4\mathrm{\varphi }$

2. $2\mathrm{\varphi }$

3. $\frac{\mathrm{\varphi }}{2}$

4. $\mathrm{\varphi }$

Q.

An arbitrary surface encloses an electric dipole. What is electric flux to the surface?

Q. Ten electrons are equally spaced and fixed around a circle of radius R. Relative to V = 0 at infinity, the electrostatic potential V and the electric field E at the centre C are

1. $V\ne 0$ and $\stackrel{\rightharpoonup }{E}\ne 0$
2. $V\ne 0$ and $\stackrel{\rightharpoonup }{E}=0$
3. $V=0$ and $\stackrel{\rightharpoonup }{E}=0$
4. $V=0$ and $\stackrel{\rightharpoonup }{E}\ne 0$

Q.

If a point charge is taken from lower potential to higher potential then PE increased or decreased?

Q.

Three particles, each having a charge of 10 micro coulomb are placed at the vertices of an equilateral triangle of side 10cm. Find the work done by a person in pulling them apart to infinite separations .

Q. Find the potential difference between $A$ and $B$

1. $70V$
2. $60V$
3. $40V$
4. $30V$

Q. A positive charge $q$ is placed in front of a conducting solid cube of side $a$ at distance $d$ from its center. Find the electric field at the center of the cube due to the charges appearing on its surface.

1. Zero
2. $\frac{Kq}{d^2}$
3. $\frac{Kq}{4d^2}$
4. $\frac{2Kq}{d^2}$

Q. In a uniform electric field, the potential is $10V$ at the origin of coordinates, and $8V$ at each of the points $(1,0,0),(0,1,0)$ and $(0,0,1)$. The potential at the point $(1,1,1)$ will be

1. $0$
2. $8V$
3. $10V$
4. $4V$

Q. A capacitor is discharging through a resistor $R$. Consider in time $t_1$, the energy stored in the capacitor reduces to half of its initial value and in time $t_2$, the charge stored reduces to one eighth of its initial value. The ratio $\frac{t_1}{t_2}$ will be

1. $\frac{1}{6}$
2. $\frac{1}{3}$
3. $\frac{1}{4}$
4. $\frac{1}{2}$

Q. Potential at the centroid of an equilateral triangle of side ‘a’, when equal charges each of magnitude ‘Q’ are placed at the vertices of the triangle is?

1. $\frac{1}{4\pi {ϵ}_0}\frac{3Q}{a}$
2. $\frac{1}{4\pi {ϵ}_0}\frac{3\sqrt{3}Q}{a}$
3. $Zero$
4. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{\sqrt{3}a}$

Q. Equal charges q are placed at the vertices A and B of an equilateral triangle ABC of side $\alpha$. The magnitude of electric field at the point C is

1. $\frac{q}{2\pi {\epsilon }_0{\alpha }^2}$
2. $\frac{\sqrt{2}q}{4\pi {\epsilon }_0{\alpha }^2}$
3. $\frac{q}{4\pi {\epsilon }_0{\alpha }^2}$
4. $\frac{\sqrt{3}q}{4\pi {\epsilon }_0{\alpha }^2}$

Q. A metal wire is bent information circle of radius 10cm. It is given a charge of 200 x 10^-6 C which spreads uniformly . Calculate the potential at its centre

Q. Two identical parallel plate capacitors A and B are connected to battery of V volts with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant K. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.

Q. A metal sphere A of radius r_{​​​​​​1} charged to a potential phi_{​​​​1} is enveloped by a thin walled conducting spherical shell B of radius r_{​​​​​​2} . Then potential phi_{​​​​2} of the sphere A after it is connected to the shell B by a thin conducting wire will be :-

Q. Three charges 2q, -q, -q are located at the vertices of an equilateral triangle. At the centre of the triangle

1. The field is zero but potential is non-zero
2. The field is non-zero but potential is zero
3. Both field and potential are zero
4. Both field and potential are non-zero

Q. Two electric charges $12\mu C$ and $-6\mu C$ are placed 20 cm apart in air. There will be a point P on the line joining these charges and outside the region between them, at which the electric potential is zero. The distance of P from $-6\mu C$ charge is

1. 0.10 m
2. 0.15 m
3. 0.20 m
4. 0.25 m

Q. Two point charges $4\mu C$ and $9\mu C$are separated by a distance of 50 cm. The potential at the point between them where the field has zero strength is

1. Zero
2. $4.5\times {10}^{5}V$
3. $9\times {10}^{5}V$
4. $9\times {10}^{4}V$

Q. In the given figure distance of the point from A where the electric field is zero is

1. 20 cm
2. 10 cm
3. None of these
4. 33 cm

Q. The minimum energy required to remove an electron is called

1. None of these
2. Work function

3. Stopping potential

4. Kinetic energy

Q. A charge Q is to be divided into two parts q and (Q-q) such that the force between them is maximum at a certain distance. The value of q is

1. $\frac{Q}{3}$
2. $\frac{Q}{2}$
3. $\frac{Q}{4}$
4. $\frac{3Q}{4}$

Q.

Two point charges q_A = 3 μC and q_B = −3 μC are located 20 cm apart in vacuum.

(a) What is the electric field at the midpoint O of the line AB joining the two charges?

(b) If a negative test charge of magnitude 1.5 × 10⁻⁹ C is placed at this point, what is the force experienced by the test charge?

Q. A cube made of insulating material has uniform charge distribution throughout its volume. Taking the electric potential due to this charged cube at infinity to be zero, the potential at the center is found to be $V_o.$ The potential at one of its corners is

1. $\frac{V_o}{8}$
2. $\frac{V_o}{4}$
3. $\frac{V_o}{2}$
4. $V_o$

Q.

A freei pitch ball of mass 6 gram carries a positive charge of (1/3 )* 10 ^{​​​​​​-7} coulomb what must be nature and magnitude of charge that should be given to second pitch ball fixed 5 cm vertically below the former baseball so that the upper bonus stationery.