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.

The dimensional formula of magnetic flux is

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 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,

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($\theta$)

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

The above plot represents the variation of induced current in a coil of $10 \mathrm{\Omega }$ resistance with time. If the current is induced due to change in magnetic flux linked with the coil, then find the magnitude of change in flux through the coil during $t=0$ to $t=5 \mathrm{s}$:

A circular loop of radius $0.3 \mathrm{cm}$ is parallel to a much bigger circular loop of radius $20 \mathrm{cm}$. Both loops are co-axial. The distance between their centres is $15 \mathrm{cm}$. If a current of $2.0 \mathrm{A}$ flows through the smaller loop, then what is the flux linked with the bigger loop?

A circular coil of wire carrying constant current $I$, forms a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by $\mathrm{\varphi }$. The magnetic flux through the area of the circular coil area is given by ${\mathrm{\varphi }}_0$. Choose correct option:

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

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). 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) ${\overrightarrow{\mathrm{B}}}_3=2\widehat{\mathrm{i}}-5\mathrm{t}\mathrm{ }\widehat{\mathrm{j}}-12\widehat{\mathrm{k}}$

Where B is in milli tesla and t is in second if the induced current in the loop due to ${\overrightarrow{\mathrm{B}}}_1,\mathrm{ }{\overrightarrow{\mathrm{B}}}_2,\mathrm{ }{\overrightarrow{\mathrm{B}}}_3$ are ${\mathrm{i}}_1,\mathrm{ }{\mathrm{i}}_2,\mathrm{ }{\mathrm{i}}_3$ respectively, then-

If the magnetic field is parallel to a surface, then the magnetic flux through the surface is

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