Magnetic Flux

The magnetic flux through each of five faces of a neutral playing dice is given ${\mathrm{\varphi }}_{\text{B}}=\pm \text{NWb}$, where N (= 1 to 5) is the number of spots on the face. The flux is positive (out-ward) for N even and negative (inward) for N odd. What is the flux through the sixth face of the die?

(i) In an a.c. generator, coil of $N$ turns and area $A$ is rotated at $v$ revolution per second in a uniform magnetic field $B$. Write the expression for the emf produced.

(ii) A $100$ turn coil of area  $0.1{\text{ m}}^{\text{2}}$  rotates at half a revolution per second. It is placed in a magnetic field $0.01 \mathrm{T}$ perpendicular to the axis of rotation of the coil. Calculate the maximum voltage generated in the coil.

A metallic horizontal ring of mass $m$ and radius $r$ falling under gravity in a region having magnetic field. If $z$ is the vertical direction, the $z$-component of magnetic field is $B_0(1+az)$ where $B_0$ and a are constants. If $R$ is the resistance of the ring, the terminal velocity of the ring is

Magnetic flux cannot be zero at any instant.

Can magnetic flux be negative?

When the current in a coil changes from $5 \mathrm{A}$ to $2 \mathrm{A}$ in $\mathrm{0}.1 \mathrm{s}$, an average voltage of $\mathrm{50\hspace{0.17em}}\mathrm{V}$ is produced. The self-inductance of the coil is

A cube of side $a$ is placed in a magnetic field of intensity $B$. The magnetic flux emerging out (outgoing flux only) of the cube will be -

A circuit consists of a coil with inductance $L$ and an uncharged capacitor of capacitance $C$. The coil is in a constant uniform magnetic field such that the flux through the coil is $\varphi$. At time $t=0 \min$, the magnetic field is abruptly switched OFF. Let ${\omega }_0=1/\sqrt{LC}$ and ignore the resistance of the circuit. Then,

A square coil of $0.01 {\mathrm{m}}^2$ area is placed perpendicular to the uniform magnetic field of intensity ${10}^3 {\mathrm{Wbm}}^{-2}$. The magnetic flux (in weber) linked with the coil is

A loop ABCDEFA of straight edges has six corner points $A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D(0, 5, 0),$ $\mathrm{E}(0, 5, 5)$ and $F(0, 0, 5)$. The magnetic field in this region is $\overrightarrow{B}=\left(3\hat{i}+4\hat{k}\right) \mathrm{T}$. The quantity of flux through the loop ABCDEFA (in $\mathrm{Wb}$) is

Which one is the correct relation between magnetic flux $\left(\varphi \right)$. magnetic field $\left(B\right)$, area surface $A$ and angle between the magnetic field lines and perpendicular distance normal to the surface area($\theta$)

A wire of infinite length carrying current $I$ lies along the z-axis. A square loop of side $\ell$ is placed such that the plane of the loop makes an angle $74°$ with the positive $x-$axis at $\left(\ell ,0,0\right)$ and side $AB$ touches the $x-$axis and parallel to $z-$axis as shown in the figure. The magnetic flux passing through the loop is $\frac{k{\mu }_0\ell }{\pi }$. Find the value of $k$. [take $I=10 \mathrm{A}, \ln \left(1.6\right)=0.47$ and $\tan 37°=\frac{3}{4}$]

A square coil of $0.01 {\mathrm{m}}^2$ area is placed perpendicular to the uniform magnetic field of intensity ${10}^3 {\mathrm{Wbm}}^{-2}$. The magnetic flux (in weber) linked with the coil is

Which of the following operations between the magnetic field and the area gives the magnetic flux?

Two concentric and coplanar rings of radius $\mathrm{r} \& \mathrm{R}$ are shown in fig. Find the magnetic flux linked through the smaller coil when same Current-$\mathrm{I}$ flow through each in opposite directions: $(\mathrm{r}<<\mathrm{R})$

A uniform magnetic field of induction $B$ is confined to cylindrical region of radius $R$. The magnetic field is increasing at a constant rate of $\frac{dB}{dt}\left(T{S}^{-1}\right)$. An electron of charge $-e$, placed at the point $P$ on the periphery of the field experiences an acceleration.

In the figure, a $120$-turn coil of radius $5 \mathrm{cm}$ and resistance $3.6 \mathrm{\Omega }$ is wrapped around a long solenoid of $250 \mathrm{turns} {\mathrm{cm}}^{-1}$ and diameter $4 \mathrm{cm}$. The axis of the coil and the axis of the solenoid make angle of $30°$ with each other. The solenoid current drops from $1.5 \mathrm{A}$ to zero in time interval $t=25 \mathrm{ms}$. Find the total charge that flows through the coil. Take ${\pi }^2\approx 10$.

Consider a coil (of area $A,$ resistance $R$ and number of turns $N$) held perpendicular to a uniform magnetic field of strength $B$. The coil is now turned through $180°$ in the time $\mathrm{\Delta }t$. Total charge that flows through a given cross-section of the coil is ...... .

A magnet is taken towards a conducting ring in such a way that a constant current of $10 \mathrm{mA}$ is induced in it. The total resistance of the ring is $0.5 \mathrm{\Omega }$. In $5 \sec$ the magnetic flux through the ring changes by :-

A charge particle moves along the line $AB$, which lies in the same plane of a circular loop of conducting wire as shown in the fig. Then :-