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.

Magnetic flux is the product of magnetic field induction and area.

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

Magnetic flux is the dot product of magnetic field induction and _____.

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?

An infinitely long cylinder is kept parallel to a uniform magnetic field $B$ direction along positive $z-$axis. The direction of induced current on the surface of cylinder a seen from the $z-$axis will be

The phase difference between the flux linked with a coil rotating in a uniform magnetic field and induced emf produced in it is

A coil of area $5 c{m}^2$ having 20 turns is placed in a uniform magnetic field of ${10}^3$ gauss. The normal to the plane of coil makes an angle ${30}^o$ with the magnetic field. The flux through the coil is

A material of 0.25 ${\mathrm{cm}}^2$ cross-sectional area is placed in a magnetic field of strength (H) 1000 $\mathrm{A} {\mathrm{m}}^{-1}$ . Then the magnetic flux produced is (Susceptibility of material is 313) (Permeability of free space, ${\mu }_0=4\pi \times {10}^{-7} \mathrm{H} {\mathrm{m}}^{-1})$

Which of the following instruments is used to measure magnetic field

In given figure, a wire loop has been bent so that it has three segments ab (a quarter circle), bc (a square corner) & ca (straight line). Here are three choices for a magnetic field through the loop






(i) ${\overrightarrow{\mathrm{B}}}_1=3\widehat{\mathrm{i}}+7\widehat{\mathrm{j}}-5\mathrm{t}\widehat{\mathrm{k}}$

(ii) ${\overrightarrow{\mathrm{B}}}_2=5\mathrm{t}\widehat{\mathrm{i}}+4\widehat{\mathrm{j}}-15\widehat{\mathrm{k}}$

(iii) ${\overrightarrow{\mathrm{B}}}_3=2\widehat{\mathrm{i}}-5\mathrm{t}\widehat{\mathrm{j}}-12\widehat{\mathrm{k}}$ where B is in milli tesllas and t is in second if the induced current in the loop due to ${\overrightarrow{\mathrm{B}}}_1\mathrm{ },\mathrm{ }{\overrightarrow{\mathrm{B}}}_2,\mathrm{ }{\overrightarrow{\mathrm{B}}}_3$ are ${\mathrm{i}}_1,\mathrm{ }{\mathrm{i}}_2,\mathrm{ }{\mathrm{i}}_3$ respectively then4

Assertion: The net magnetic flux coming out of a closed surface is always zero.

Reason: Unlike poles of equal strength exist together.

Assertion: The magnetic flux through a closed surface is zero

Reason: Gauss's law is applied in the case of electric flux only

A uniform but time varying magnetic field exists in cylindrical region and directed into the paper. If field decrease with time and a positive charge placed at any point inside the region. Then it moves -

   

A uniform current carrying ring of mass m and radius $\mathrm{R}$ is connected by a massless string as shown. A uniform magnetic field ${\mathrm{B}}_0$ exist in the region to keep the ring in horizontal position, then the current in the ring is $\left(\mathcal{l}=\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{ }\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}\right)$ -

The magnetic flux through a coil varies with time $\mathrm{t}$ as shown in diagram. Which graph best represents the variation of the emf $\mathrm{E}$ induced in the coil ?