Introducing Flux

Q. what is looping the loop concept?

Q. Find the flux through a sphere of radius R centred at the origin due to the E-field $\overrightarrow{E}=a\left(\frac{x\hat{i}+j\hat{j}}{x^2+y^2}\right)$

1. $4\pi \alpha R$
2. zero
3. $\pi \alpha R$
4. $2\pi \alpha R$

Q. Consider a thin spherical shell of radius $R$ with its centre at origin, carrying a uniform positive charge. The variation of electric field $\overrightarrow{E}\left(r\right)$ and electric potential $V\left(r\right)$ with radial distance $r$ from the centre is given by

1. 
2. 
3. 
4. 

Q. A ball of radius R carries a positive charge whose volume density depends only on a separation r from the ball’s centre as $\rho ={\rho }_0(1-\frac{r}{R})$, where ${\rho }_0$ is a constant. Assuming the permittivities of the ball and the environment to be equal to unity, find the ratio of the magnitude of the electric field strength inside the sphere to that of the outside.

1. $\frac{1}{R^3}(r-\frac{3r^2}{4R})$
2. $\frac{1}{R^3}(r^3-\frac{3r^4}{4R})$
3. $\frac{4}{R^3}(r^3-\frac{3r^4}{4R})$
4. 1

Q. Flux due to $q$ through square plate is

1. $\frac{q}{6{ϵ}_o}$
2. $\frac{q}{6{ϵ}_o}$
3. $\frac{q}{12{ϵ}_o}$
4. $\frac{q}{24{ϵ}_o}$

Q. A charge of 1 C is located at the center of the sphere of radius 10 cm and a cube of side 20 cm. The ratio of outgoing flux through the sphere and th cube is.

Q. A cube has sides of length $l=0.300m$. It is placed with one corner at the origin as shown in the
figure. The electric field is not uniform, but it is given by $\overrightarrow{E}=(-5.00N{C}^{-1})x\hat{i}+\left(3.00N{C}^{-1}\right)z\hat{k}$.
The total flux passing through the cube is

1. $-0.135N{m}^2{C}^{-1}$
2. $-0.054N{m}^2{C}^{-1}$
3. $-0.081N{m}^2{C}^{-1}$
4. Zero

Q. A cube has sides of length L = 0.300 𝑚. It is placed with one corner at the origin as shown in the
figure. The electric field is not uniform, but it is given by $\overrightarrow{E}=(-5.00N{C}^{-1})x\hat{i}+\left(3.00N{C}^{-1}\right)z\hat{k}$.
The total electric charge inside the cube is

1. $-0.054{\in }_{0}C$
2. $0.081{\in }_{0}C$
3. $0.135{\in }_{0}C$
4. $0.054{\in }_{0}C$

Q.

Statement 1: The flux of a point charge ‘q’ located at origin, is positive through a point p (1, 2, 4)

Statement 2: The flux of a point charge ‘q’ located at origin is negative through a point P (1, 2, 4)

1. 1 is true, 2 is true and 2 is the correct explanation for 1

2. 1 is true, 2 is true but 2 is not the correct explanation for 1

3. 1 is true, 2 is false

4. 1 is false and 2 is false

Q.

Electric field in the given region is vertically downwards. An open hemisphere of radius $a$ is placed as shown. Find the net flux of electric field through the curved surface of hemisphere.

1. 0

2. $E\pi a^2$

3. $2E\pi a^2$

4. $4E\pi a^2$

Q. Equipotential surface associated with an electric field which is increasing in magnitude along the $x-$ direction are

1. Planes parallel to $YZ-$ plane
2. Coaxial cylinders of increasing radii around $x-$ axis.
3. Planes parallel to $XY-$ plane
4. Planes parallel to $XZ-$ plane

Q. A cube has sides of length L = 0.300 𝑚. It is placed with one corner at the origin as shown in the
figure. The electric field is not uniform, but it is given by $\overrightarrow{E}=(-5.00N{C}^{-1})x\hat{i}+\left(3.00N{C}^{-1}\right)z\hat{k}$.
The total electric charge inside the cube is

1. $-0.054{\in }_{0}C$
2. $0.081{\in }_{0}C$
3. $0.135{\in }_{0}C$
4. $0.054{\in }_{0}C$

Q.

A hollow prism with side ABCD as open is kept in a region of electric field E. The field is parallel to the sides. BEC and AFD. Find the flux coming out of the pyramid?

1. $Ela$

2. $0$

3. $2Elacos{30}^0$

4. None of these

Q.

Flux is a __ (Scalar/vector) quantity.

Q. What is the difference between solid non conducting sphere and Thin charged conducting spherical shell

Q. A cube has sides of length L = 0.300 𝑚. It is placed with one corner at the origin as shown in the
figure. The electric field is not uniform, but it is given by $\overrightarrow{E}=(-5.00N{C}^{-1})x\hat{i}+\left(3.00N{C}^{-1}\right)z\hat{k}$.


The surfaces that have zero flux are

1. $S_2,S_4$ and $S_5$
2. $S_1,S_3,S_4$ and $S_6$
3. $S_1,S_2$ and $S_3$
4. $S_2,S_3$ and $S_4$

Q.

A conic surface is placed in a uniform electric field $E$ as shown such that field is perpendicular to the surface on the side AB. The base of the cone is of radius $R$ and height of the cone is $h$. The angle of cone is $\theta$ as shown. Find the magnitude of that flux which enters the cone's curved surface on the left side. Don’t count the outgoing flux.

1. $ER(hcos\theta +\frac{\pi Rsin\theta }{2})$

2. $ER(hsin\theta +\frac{\pi Rcos\theta }{2})$

3. $ER(hcos\theta +\frac{\pi Rsin\theta }{3})$

4. $ER(hsin\theta +\frac{\pi Rsin\theta }{2})$

Q.

A constant Electric field $\overrightarrow{E}=2\hat{i}$ exists in space. The electric flux through a square surface of side 2m with its surface tilted 60⁰ from the y axis is$4\frac{N{m}^2}{C}$.

1. True

2. False