Infinite Line of Charge

Q. Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure :

1. $\sqrt{3}ql\frac{\hat{j}-\hat{i}}{\sqrt{2}}$
2. $2ql\hat{j}$
3. $-\sqrt{3}ql\hat{j}$
4. $\left(ql\right)\frac{\hat{j}-\hat{i}}{\sqrt{2}}$

Q. Find the electric field vector at P(a, a, a) due to three infinitely long lines of charges along the x, y and z axis, respectively. The charge density i.e. charge per unit length of each wire is $\mathrm{\lambda .}$

1. $\frac{\lambda }{3{\mathrm{\pi \epsilon }}_{0}a}\left(\hat{i}+\hat{j}+\hat{k}\right)$
2. $\frac{\lambda }{2{\mathrm{\pi \epsilon }}_{0}a}\left(\hat{i}+\hat{j}+\hat{k}\right)$
3. $\frac{\lambda }{2\sqrt{2}{\mathrm{\pi \epsilon }}_{0}a}\left(\hat{i}+\hat{j}+\hat{k}\right)$
4. $\frac{\sqrt{2}\lambda }{{\mathrm{\pi \epsilon }}_{0}a}\left(\hat{i}+\hat{j}+\hat{k}\right)$

Q. 25.The electrostatic potential difference between points A and B, V(A)-V(B), which are distances r(A)=2m and r(B)=1m from an infinitely long thin wire with linear charge density equal to 1 microC is?

Q. A sphere of radius 5cm has acharge of 31.41micro coulomb calculate the surface density of charge

Q. Two charges +6 μC and –4μC are placed 15 cm apart as shown. At what distance from A to its right on the line joining point A and B, the electrostatic potential is zero (distance in cm) A B +6 × 10 C –6 –4 × 10 C –6 15 cm (1) 4, 9, 60 (2) 9, 45, infinity (3) 20, 45, infinity (4) 9, 15, 45

Q.

What is the dimensional formula of the permittivity of a vacuum?

Q. An electric dipole is placed at a distance x from center $O$ on the axis of a charged ring of radius $R$ and charge $Q$ uniformly distributed over it. What is the work done in rotating the dipole through ${180}^{\circ }$?

1. $\frac{aqQx}{2\pi {\epsilon }_0(R^2+x^2{)}^{\frac{3}{2}}}$
2. $\frac{aqQx}{\pi {\epsilon }_0(R^2+x^2{)}^{\frac{3}{2}}}$
3. $aqQx(R^2+x^2)$
4. zero

Q. 68.Uniform vertical electric field is estabilished in the space between two large plate large parallel plate . A small conducting sphere of mass m is suspended in the electric field from a string of length L. if the sphere is given (a + q) charge and lower plate is charged positively the time period of oscillation of this

Q.

Region surrounding oscillating electric dipole has which kind of field?

Q. A large charged metal sheet is placed in a uniform electric field, perpendicular to the electric field lines. After placing the sheet into the field, the electric field on the left side of the sheet is $E_1=5\times {10}^{5}V{m}^{-1}$ and on the right it is $E_2=3\times {10}^{5}V{m}^{-1}$. The sheet experience a net electric force of 0.08 N. Find the area of one face of the sheet. Assume the external electric field to remain constant after introducing the large sheet. Use $\left(\frac{1}{4{\mathrm{\pi \epsilon }}_0}\right)=9\times {10}^{9}N{m}^2{C}^{-2}$

1. $3.6\pi \times {10}^{-2}{m}^{-2}$
2. $0.9\pi \times {10}^{-2}{m}^{-2}$
3. none of these
4. $1.8\pi \times {10}^{-2}{m}^{-2}$

Q.

An infinite line charge produces a field of $9\times {10}^{4}N/C$ at a distance of 2cm. Calculate the linear charge density.

Q.

The dipole moment per unit volume is called

1. Surface charge density

2. Polarization

3. Linear charge density

4. Volume charge density

Q. Find the Flux through the rectangular piece of area $10\text{cm}\times 20\text{cm}$, when placed in a uniform electric field intensity of $200\text{N/C}$ as shown in figure.

1. $4{\text{Nm}}^2{\text{C}}^{-1}$
2. $3.5{\text{Nm}}^2{\text{C}}^{-1}$
3. $2.5{\text{Nm}}^2{\text{C}}^{-1}$
4. Zero

Q.

What do electric field lines provide information about?

Q. A point charge $q$ is surrounded by eight fixed identical point charges at the same distance $r$ as shown in figure. How much work will be done by external force to remove point charge $q$ from centre $O$ to infinity very slowly?

1. $\frac{-2q^2}{\pi {ϵ}_{0}r}$
2. $\frac{+2q^2}{\pi {ϵ}_{0}r}$
3. $0$
4. $\frac{-4q^2}{\pi {ϵ}_{0}r}$

Q. 12.Two concentric metallic spherical shells are given equal amount of positive charges.Then a)the outer sphere is always at higher potential b)the inner sphere is always at higher potential c)both the spheres are at the same potential d)no prediction can be made about the potential unless the actual value of charges and radii are known

Q.

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 × 10⁻²² C/m². What is E: (a) in the outer region of the first plate, (b) in the outer region of the second plate, and (c) between the plates?

Q. A charge $q$ is moved from point $A$ to point $B$ in an uniform electric field along $4$ paths as shown below. The work done to move the charge along the paths is $W_1,W_2,W_3\text{and}{W}_4$ respectively. Choose the correct statement.

1. $W_4>W_1>W_2>W_3$
2. $W_4<W_1<W_2<W_3$
3. $W_4=W_1=W_2=W_3$
4. $W_4<W_1=W_2<W_3$

Q. Electric field in a region is given as $\overrightarrow{E}=(10-5x)\hat{i}$. A charged particle of mass $5\text{kg}$ and charge $Q=1\text{C}$ is situated at origin and free to move in the given electric field. Then choose the correct options.

1. Motion of the charged particle is oscillatory
2. Maximum displacement of charge particle from origin is $4\text{SI units}$
3. Maximum velocity gain by charge particle is $2\text{SI units}$ units.
4. The position of charge particle, when velocity gained by particle is maximum, is $2\text{SI units}$.

Q. Consider a uniform solid sphere of charge Q and radius R. What is the electrostatic potential energy stored in the region O<=r