Physics NCERT Exemplar Solutions Class 12th Chapter Six

Sol. (n) $\lambda =5$

$(\mathrm{n},\mathrm{m})$ : Integers

$\begin{array}{rr}& \left(\frac{2m+1}{2}\right)\lambda =\frac{3}{2}\\ & \Rightarrow \mathrm{}\frac{3/2}{5}=\frac{2m+1}{2n}\\ & \Rightarrow \mathrm{}3n=10m+5\end{array}$

$\mathrm{N},\mathrm{m}$ are integers.

So,  $\mathrm{m}=1,\mathrm{}\mathrm{n}=5,\mathrm{}\lambda =1$

$\begin{array}{lll}\mathrm{m}=4& \mathrm{n}=15& \lambda =\frac{1}{3}\\ \mathrm{m}=7& \mathrm{n}=25& \lambda =\frac{1}{5}\end{array}$

$tan\delta =\frac{B_v}{B_h}$

$Bv=B_{h}tan45$                

= 4 * 10^-3

emf induced in the rod is = $B_{v}v\mathcal{l}$  

$=4*10^{-3}*20*\frac{20}{100}$                

$\begin{array}{l}=16*10^{-3}\\ =16mv\end{array}$                 

Students can expect conceptual questions on Faraday's and Lenz's Laws, derivations involving EMF, flux calculations, and application-based questions like the functioning of generators or transformers. Numerical problems involving   and time-varying magnetic fields are also frequently included.

Lenz's law is used for devices like eddy current brakes, induction cooktops, and metal detectors. For example in induction cooktops, the currents in the cookware are induced by the changing magnetic fields. It generates the heat due to resistance. It is based on Lenz's law which follows the opposing nature of the induced current.

The negative sign in Faraday's Law of Electromagnetic Induction is extremely significant as it gives the direction of the induced EMF. Faraday's law is based on Lenz's law which reflects the principle of conservation of energy. It says that the induced EMF always opposes the magnetic flux changes that cause it. Following is the Faraday's law equation:

This is a multiple choice answer as classified in NCERT Exemplar

(a, d) When circular coil expands radially in a region of magnetic field such that the magnetic field is in the same plane as the circular coil or the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably in such a way that the cross product of magnetic field and surface area of plane of coil remain constant at every instant.

This is a multiple choice answer as classified in NCERT Exemplar

(a, d) Mutual inductance of a coil increases when they came closer also the relation for the same will be given by

M₂₁= ${\mu }_0$ n₁n₂ r₁²l= M₁₂

M₂₁= M₁₂=M

This is a multiple choice answer as classified in NCERT Exemplar

(a, b, c) Here, magnetic flux linked with the isolated coil change when the coil being in a time varying magnetic field, the coil moving in a constant magnetic field or in time varying magnetic field.

This is a multiple choice answer as classified in NCERT Exemplar

(a, b, d) A metal plate is getting heated when a DC or AC current is passed through the plate, known as heating effect of current. Also, when metal plate is subjected to time varying magnetic field, the magnetic flux linked with the plate changes and eddy currents comes into existence which make the plate hot.

This is a multiple choice answer as classified in NCERT Exemplar

(b) The self-inductance of a long solenoid of cross-sectional area A and length l, having n turns per unit length, filled the inside of the solenoid with a material of relative

permeability (e g. ., soft iron, which has a high value of relative permeability) is given by the relation L = ${\mu }_r{\mu }_o$ n²A/l