Magnetic Flux

Q. The flux of a magnetic field over a closed surface is zero.

1. False
2. True

Q. A small equilateral triangular loop of side $l=1cm$ is kept inside a large circular loop of radius r such that both are coplanar and concentric. If current in the larger loop is as shown in the graph, then find the current induced in the smaller loop during the time instants given. Take anticlock wise current as positive.


List - 1 gives time instants and list - 2 gives induced current in the smaller loop. Take $\frac{{\mu }_0\pi }{2rR}=1$ where R is resistance of small loop.
$\begin{array}{cccc}& \text{List -1}& & \text{List -2}\\ \left(I\right)& 0sec& \left(p\right)& 25\mu A\\ \left(II\right)& \frac{1}{3}sec& \left(Q\right)& 12.5\mu A\\ \left(III\right)& \frac{3}{2}sec& \left(R\right)& 0\mu A\\ \left(IV\right)& \frac{5}{3}sec& \left(S\right)& -6.25\mu A\\ & & \left(T\right)& -12.5\mu A\\ & & \left(U\right)& -25\mu A\end{array}$

1. $I\to P,II\to Q,III\to R,IV\to T$
2. $I\to U,II\to S,III\to R,IV\to T$
3. $I\to P,II\to Q,III\to T,IV\to R$
4. $I\to U,II\to T,III\to R,IV\to T$

Q. A small circular loop of radius $l=1cm$ is kept inside a larger circular loop of radius r such that both are coplanar and concentric. If the current in larger loop is as shown in the graph, then current induced in the smaller loop any time is represented as $I_n$ at any instant. Take anticlockwise current as positive. List -1 contains time instants, and List-2 contains the values for $I_n$. Match them. Take $\frac{{\mu }_0\pi }{2Rr}=1$.

$\begin{array}{cccc}& \text{List -1}& & \text{List -2}\\ \left(I\right)& 0sec& \left(p\right)& 25\mu A\\ \left(II\right)& \frac{1}{3}sec& \left(Q\right)& 12.5\mu A\\ \left(III\right)& \frac{3}{2}sec& \left(R\right)& 0\mu A\\ \left(IV\right)& \frac{5}{3}sec& \left(S\right)& -6.25\mu A\\ & & \left(T\right)& -12.5\mu A\\ & & \left(U\right)& -25\mu A\end{array}$

1. $I\to P,II\to R,III\to U,IV\to P$
2. $I\to P,II\to R,III\to P,IV\to P$
3. $I\to U,II\to R,III\to P,IV\to U$
4. $I\to U,II\to R,III\to U,IV\to U$

Q. A square coil ${10}^{-2}{\text{m}}^2$ area is placed with its plane perpendicular to a uniform magnetic field of intensity ${10}^3{\text{Wb/m}}^2.$ The magnetic flux through the coil is

1. $10\text{Wb}$
2. ${10}^{-5}\text{Wb}$
3. ${10}^5\text{Wb}$
4. $100\text{Wb}$

Q. The flux of $\overrightarrow{B}$ through any closed surface is :

1. $>0$
2. $<0$
3. $=0$
4. $>0$

Q. Which of the following statements regarding magnetic lines of force is correct?

1. Total magnetic flux linked with a closed surface is always zero
2. They need not be perpendicular to the surface from where they start of whre they meet
3. They may or may not pass through a conductor
4. All of these

Q. A closed surface $S$ encloses a magnet of magnetic moment $2ml$. The magnetic flux emerging from the surface is :

1. ${\mu }_{0}m$
2. $2{\mu }_{0}m$
3. Zero
4. $2m/{\mu }_0$

Q. What is Gauss's law in magnetism? What does it represent?

Q. If three identical bar magnets each of magnetic moment 'M' are arranged in the form of an equilateral triangle such that unlike poles are in contact. The result magnetic moment is:

1. $\sqrt{3}M$
2. $\frac{M}{3}$
3. $2M$
4. Zero

Q. In the Bohr model of hydrogen atom, the electron circulates around the nucleus in a path of radius $5.1\times {10}^{-11}m$ at a frequency $6.8\times {10}^{15}{s}^{-1}$. Find the magnetic field set up at the centre of the orbit.