Karnataka Board PUCPUC Science 2nd PUC Class 12

Find the Mutual Inductance Between the Straight Wire and the Square Loop of Figure. - Physics

Advertisements
Advertisements
Sum

Find the mutual inductance between the straight wire and the square loop of figure.

Advertisements

Solution

The flux through the square frame is given by `phi=Mi`

Let us first calculate the flux through the square frame.

Let us now consider an element of loop of length dx at a distance x from the wire.

Now,

Area of the element of loop, A = adx

Magnetic field at a distance x from the wire,

\[B = \frac{\mu_0 i}{2\pi x}\]

The magnetic flux of the element is given by

\[d\phi = \frac{\mu_0 i \times adx}{2\pi x}\]

The total flux through the frame is given by

\[\phi = \int d\phi\]

\[       =  \int_b^{a + b} \frac{\mu_0 iadx}{2\pi x}\]

\[       = \frac{\mu_0 ia}{2\pi}\ln\left[ 1 + \frac{a}{b} \right]\]

Also,

\[\phi = Mi\]

Thus, the mutual inductance is calculated as

\[Mi = \frac{\mu_0 ia}{2\pi}\ln\left[ 1 + \frac{a}{b} \right]\]

\[ \Rightarrow M = \frac{\mu_0 a}{2\pi}\ln\left[ 1 + \frac{a}{b} \right]\]

  Is there an error in this question or solution?
Chapter 16: Electromagnetic Induction - Exercises [Page 313]

APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 16 Electromagnetic Induction
Exercises | Q 95 | Page 313

RELATED QUESTIONS

The co-efficient of mutual induction between primary and secondary coil is 2H. Calculate induced e.m.f. if current of 4A is cut off in 2.5 x 10-4 seconds


If the radius of a sphere is doubled without changing the charge on it, then electric flux originating from the sphere is ______.


Define mutual inductance.


Explain the meaning of the term mutual inductance.


Explain self induction and mutual induction


Define coefficient of mutual induction. 


Explain the phenomenon of mutual induction.


A coil of self-inductance 2.5H and resistance 20Ω is connected to a battery of emf 120V having the internal resistance of 5 n. Find:

1) The time constant of the circuit.

2) The current in the circuit in steady state


Two circular loops are placed with their centres separated by a fixed distance. How would you orient the loops to have (a) the largest mutual inductance (b) the smallest mutual inductance?


Find the mutual inductance between the circular coil and the loop shown in figure.


The current in a long solenoid of radius R and having n turns per unit length is given by i= i0 sin ωt. A coil having N turns is wound around it near the centre. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid ant the coil.


A solenoid of length 20 cm, area of cross-section 4.0 cm2 and having 4000 turns is placed inside another solenoid of 2000 turns having a cross-sectional area 8.0 cm2 and  length 10 cm. Find the mutual inductance between the solenoids.


A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 10 A in 0.2 s, what is the change of flux linkage with the other coil?


An emf of 96.0 mV is induced in the windings of a coil when the current in a nearby coil is increasing at the rate of 1.20 A/s. What is the mutual inductance (M) of the two coils?


A long solenoid of length l, cross-sectional area A and having N1 turns (primary coil), has a small coil of N2 turns (secondary coil) wound about its center. Determine the Mutual inductance (M) of the two coils.


The mutual inductance of two coils is 10 mH. If the current in one of the coil changes from 5 A to 1 A in 0.2 s, calculate the emf induced in the other coil. Also calculate the induced charge flowing through the coil if its resistance is 5 Ω.


A pair of the adjacent coil has a mutual inductance of 1.5 H. If the current in one coil varies from 0 to 20 A in 0.5 s, what is the change of flux linked with the other coil. 


Define Mutual Inductance.


The dimensions of self or mutual inductance are given as ______.


In mutual induction, the main current remains same because ____________.


In an induction coil, the coefficient of mutual inductance is 6 henry. If a current of 10 ampere in the primary coil is cut-off in `1/1500"s"`, the e.m.f. at the terminals of the secondary coil will be ____________.


An alternating current of frequency 200 rad/s and peak value 1 A is applied to the primary of a transformer. If the coefficient of mutual induction between the primary and the secondary is 1.5H, then the voltage induced in the secondary will be approximately (π = 2217)


A coil of radius 'r' is placed on another coil (whose radius is 'R' and current flowing through it is changing) so that their centres coincide. (R>>r) if both the coils are coplanar then the mutual inductance between them is proportional to ______.


Alternating current of peak value `(2/pi)` ampere flows through the primary coil of transformer. The coefficient of mutual inductance between primary and secondary coil is 1 H. The peak e.m.f. induced in secondary coil is ______. (Frequency of a.c. = 50 Hz)


Two coils P and Q have mutual inductance 'M' H. If the current in the primary is I = I0 sin `omega`t, then the maximum vlaue of e.m.f. indued in coil Q is ____________.


The mutual inductance between two coils is 0.09 henry. If the current in the primary coil changes from 0 to 20 A in 0.006 s, the e.m.f. induced in the secondary coil at that instant is ____________.


The coefficient of mutual inductance is 2H and induced e.m.f. across secondary is 2 kV. Current in the primary is reduced from 6 A and 3A. The time required for the change of current is ____________.


The mutual inductance of a pair of coils is 0.75 H. If current in the primary coil changes from 0.5 A to zero in 0.01 s, find average induced e.m.f. in secondary coil ______.


The mutual inductance between two coils depends on ______.

Mutual induction is the production of induced e.m.f. in a coil due to the changes of current in the ______.

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon the ______.


Two circular coils have their centres at the same point. The mutual inductance between them will be maximum when their axes ______


Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 > > R2, the mutual inductance M between them will be directly proportional to ______.


Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to ______.


An emf of 91 mV is induced in the windings of a coil when the current in o nearby coil is increasing at the rate of 1.3 A/s. what is the mutual inductance (M) of the two coils in mH?


A plane loop is shaped in the form as shown in figure with radii a = 20 cm and b = 10 cm and is placed in a uniform time varying magnetic field B = B0 sin ωt, where B0 = 10 mT and ω = 100 rad/s. The amplitude of the current induced in the loop if its resistance per unit length is equal to 50 × 10-3 Ω/m. The inductance of the loop is negligible is ______ A.


Write the S.I. unit of mutual inductance.


The mutual inductance of a pair of adjacent coils is 1.5 H. If the current is one coil changes from 5 A to 10 A in 0.1 s, the rate of change of magnet flux linkage is ______.


A rectangular coil of wire 50 turn each of area 6 x 10-4 m2 is freely suspended in a field of 3 x 10-2 Wb / m2. Calculate the current flowing through the coil when it deflects through 60°, when torsional constant is 3.82 x 10-6 SI unit.


State and define the SI unit of mutual inductance.


Two coils having self inductances L1 = 75 mH and L2 = 55 mH are coupled with each other. The coefficient of coupling (K) is 0. 75. Calculate the mutual inductance (M) of the two coils


Share
Notifications



      Forgot password?
Use app×