Surface Integral

Q.

a point charge q is placed at the corner of a cube with side l find flux through entire surface and flux through each face

Q. The figure shows a closed dotted surface which intersects a conducting uncharged sphere. If a positive charge is placed at the point $P$, the flux of the electric field through the closed surface

1. will remain zero.
2. will become positive.
3. will become negative.
4. data insufficient

Q.

The electric field in a region is given by $\left(\frac{3}{5}{E}_{\circ }\hat{i}+\frac{4}{5}{E}_{\circ }\hat{j}\right)$. The ratio of the flux of the reported field through the rectangular surface of area $0.2m^2$ (parallel to y-z plane) to that of the surface of area $0.3m^2$(parallel to x-z plane) is $a:2$, where a = ________

Q. A long hollow cylinder has linear charge density lamda. What is the electric field at a radial distance r outside the cylinder?

Q.

Why dont the electric field lines cross?

Q. The length of each side of cubical closed surface is l. If charge q is situated on one of the vertices of the cube, then the flux passing through each face the cube will be

Q. A charge q is distributed uniformly on the surface of a sphere of radius R it is covered by a concentric hollow conducting sphere of radius 2R charge on the outer surface of the hollow sphere will be if it is earthed

Q. The ratio of magnetic field at the centre of the coil of radius $R$ and at a distance $3R$ on its axis is

1. $10\sqrt{10}$
2. $20\sqrt{10}$
3. $2\sqrt{10}$
4. $\sqrt{10}$

Q. A long string with a charge of $\lambda$ per unit length passes through an imaginary cube of edge $l$. The maximum possible flux of the electric field through the cube will be

1. $\frac{\sqrt{2}\lambda l}{{ϵ}_0}$
2. $\frac{6\lambda l^2}{{ϵ}_0}$
3. $\frac{\sqrt{3}\lambda l}{{ϵ}_0}$
4. $\frac{\lambda l}{{ϵ}_0}$

Q. A ring of radius $R$ is made out of a thin metallic wire of area of cross section $A$. The ring has a uniform charge $Q$ distributed on it. A charge $q_0$ is placed at the centre of the ring. If $\text{Y}$ is the young`s modules for the material of the ring and $\Delta R$ is the change is the radius of the ring then find $\Delta R.$

1. $\frac{q_{0}Q}{8{\pi }^2{\epsilon }_{0}RA\text{Y}}$
2. $\frac{q_{0}Q}{8{\pi }^2{\epsilon }_0^{2}RA\text{Y}}$
3. $\frac{q_{0}Q}{4{\pi }^2{\epsilon }_{0}RA\text{Y}}$
4. $\frac{q_{0}Q}{4\pi {\epsilon }_{0}RA\text{Y}}$

Q. 36.A charge particle q is placed at the centre of o of cube side L (ABCDEFGH). Another same charge q is placed at a distance L from the centre o. Then what is the electric flux through the side ABCD? The picture is attached with it.

Q. A charge of $9\times {10}^{-8}\text{C}$ is distributed uniformly on the surface of a sphere of radius $1\text{cm}$. It is covered by a concentric, hollow conducting sphere of radius $5\text{cm}$. Find the electric flux through the hollow sphere.
(Take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$)

1. ${10}^2{\text{N-m}}^2/\text{C}$
2. ${10}^3{\text{N-m}}^2/\text{C}$
3. ${10}^4{\text{N-m}}^2/\text{C}$
4. ${10}^5{\text{N-m}}^2/\text{C}$

Q. 69.An infinite sheet of width d is lying in a horizontal plane . A point charge q is kept at a perpendicular sepration of d/2 from the centre of the sheet. Electric flux due to this point charge q passing through the given sheet is

Q. A point charge $q_1$ is placed inside cavity $1$ and another point charge $q_2$ is inside cavity $2$. If a point charge $q$ is placed outside the conductor then the charge on outer surface of the conductor would be

1. $Q+q_1+q_2$ and it is non-uniformly distributed.
2. $Q+q_1+q_2$ and its uniform or non-uniform distribution depending upon locations of $q_1$ and $q_2$.
3. $Q+q_1+q_2$ and would be distributed uniformly.
4. $Q+q_1+q_2$ and the distribution depends upon the locations of $q_1,q_2$ and $q$.

Q. What is the flux through one face of a cube of side a if a point charge q is at one of its corner?
What is the contribution of charge placed at one of the corner in cube?

Q.

The unit of the Poynting vector is ______

Q. 123.The linear charge density on the circumference of a circle of radius A varies as d=dcos theta . The total charge on it is?

Q. Choose the correct statement regarding electric lines of force

1. They emerged from negative charge and terminate at positive charge.
2. The electric field in that region is weak where the density of electric lines of force are more.
3. They are in radial directions for a point charge.
4. The have a physical existence.

Q. A charge $Q$ is distributed uniformly on a ring of radius $r$. A sphere of equal radius $r$ is constructed with it's centre at the periphery of the ring. Find the flux of the electric field through the surface of the sphere.

1. $\frac{Q}{{ϵ}_0}$
2. $\frac{Q}{2{ϵ}_0}$
3. $\frac{Q}{3{ϵ}_0}$
4. $\frac{Q}{4{ϵ}_0}$

Q. Assertion$\left(A\right)$: In a region where, uniform electric field exists, the net charge within a volume of any size is zero.

Reason$\left(R\right)$: Net electric flux within any closed surface in the region of uniform electric field is zero.

Select the most appropriate answer from the options given below

1. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
2. Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
3. $A$ is true but $R$ is false
4. $A$ is false and $R$ is also false

Q. Soft iron used to make the core of transformer, because of its :

1. low coercivity and high retentivity
2. high coercivity and low retentivity
3. high coercivity and high retentivity
4. low coercivity and low retentivity

Q.

Pick out the statement which is incorrect.

1. A negative test charge experiences a force opposite to the direction of the field.

2. The tangent drawn to a line of force represents the direction of electric field.

3. Field lines never intersect.

4. The electric field lines forms closed loop.

Q. When does a charged circular loop behave as a point charge?

Q. Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. Then the net charge on the sphere will be

1. Negative and distributed uniformly over its surface.
2. Negative and appears only at the point on the sphere which is closest to the point charge.
3. Negative and distributed non-uniformly over the entire surface of sphere.
4. Zero

Q. 134. Figure shows a long thread along the axis of a long Hollow cylinder the uniform charge per unit length of thread is lamda while the uniform charge density of the cylinder is -sigma the radius of the cylinder is R . Total fluxe associated with coaxial cylinder of finite length and radius twice that of charged cylinder is zero if the magnitude of sigma is

Q. A smooth tunnel is made in a sphere of radius R along its diameter. The uniform volume charge density is rho. A charge sphere particle of mass m and charge -q is placed at the centre of the sphere. The time period of motion of -q when displaced by small displacement from its centre is

Q. What is the electric field at a point P(at dis†an ce 3r from centre) due to induced charge on the outer surface of a conducting sphere if a charge q is kept inside the sphere ^{}at r/2 from the centre.(r is radius of sphere)

Q. Assertion :Four point charges $q_1$, $q_2$, $q_3$ and $q_4$ are as shown in figure. The flux over the shown Gaussian surface depends only on charges $q_1$ and $q_2$. Reason: Electric field at all points on Gaussian surface depends only charges $q_1$ and $q_2$.

1. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3. Assertion is correct but Reason is incorrect.
4. Assertion is incorrect but Reason is correct.

Q. 78. 3 equal point charges of charge + q each are moving along a circle of radius r and a point charge - 2q is placed at the centre of the circle if charges are revolving with constant and same speed in the circle then calculate the speed of the charges

Q. Q) TWO CHARGES -2q AND +q ARE LOCATED AT (-a, 0) AND (4a, 0) . CALCULATE THE ELECTRIC FLUX THROUGH A SPHERE OF RADIUS 3a , WITH ITS CENTRE AT ORIGIN.