Q25 of 26 Page 1

(i) Express Biot-Savart law in the vector form.
(ii) Use it to obtain the expression for the magnetic field at an axial point, distance d from the center of a circular coil of radius R OR current I.
(iii) Also, find the ratio of the magnitudes of the magnetic field of this coil at the center and at an axial point for which x S R 3 .

OR



(a) Consider a beam of charged particles moving with varying speeds. Show how crossed electric and magnetic fields can be used to select charged particles of a particular velocity?
(b) Name another device/machine which uses crossed electric and magnetic fields. What does this machine do and what are the functions of magnetic and electric fields in this machine? Where do these field exist in this machine? Write about their natures.


(i) The vector form of Biot-Savart Law is given by


Hence the direction is perpendicular to dl and r and is given by the right hand corkscrew rule.



(ii) Let us consider a coil of radius R, carrying current I. We wish to find the magnetic field at point P as shown in the figure.


Here, distance AP is calculated using Pythagoras theorem.


The loop lies in the y-z plane and we wish to calculate the magnetic field along the x-axis. The Biot-savart law is



Consider an element dl on the loop and a position vector r which lies on the x-y plane. Hence, dl and r are perpendicular to each other (

More from this chapter

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22

(i) Mention two properties of soft iron due to which it is preferred for making an electromagnet.
(ii) State Gausss law in magnetism. How is it different from Gausss law in electrostatics and why?

OR


Derive an expression for the axial magnetic field of a finite solenoid of length 2l and radius r carrying current I. Under what condition does the field become equivalent to that produced by a bar magnet?


 23

During a thunderstorm the live wire of the transmission line fell down on the ground. A group of boys passing through noticed it and some of them wanted to place the wire by the side. As they were approaching the wire and trying to lift it, Hari noticed it and immediately pushed them away to prevent them from touching the wire. Two of them got hurt in the process. Hari took them to a doctor to get medical aid.

Based on the above paragraph, answer the following:


(a)Write two values which Hari displayed during the incident.
(b) Why is it that a bird can sit over a suspended live wire without any harm whereas touching it on the ground can give a fatal shock?
(c) The electric power from a power plant is set up to a very high voltage before transmitting it to distant consumers. Write the reason for it.


 24

(i) Find the magnitude and direction of current in 1 V resistor in the given circuit.


(ii)Two student’s X and Y perform an experiment on potentiometer separately using the circuit diagram shown below.



Keeping other things unchanged (a) X increases the value of resistance R, (b) Y decrease the value of resistance S in the set up. How will these changes affect the position of null point in each case and why?


OR



(a) Use Kirchhoff’s rules, calculate the current in the arm AC of the given circuit.
(b) On what principle does the meter bridge work? Why are the metal strips used in the bridge?


 26

When a parallel beam of monochromatic source of light of wavelength l is incident on a single slit of width a, show how the diffraction pattern is formed at the screen by the interference of the wavelets from the slit. Show that, besides the central maximum at u50, secondary maxima are observed at and the minima at

Why do secondary maxima get weaker in intensity with increasing n? Explain.


OR


(i) Draw a ray diagram showing the geometry of formation of image of a point object situated on the principal axis and on the convex side of a spherical surface of radius of curvature R. Taking the rays as incident from a rarer medium of refractive index n1 to a denser medium of refractive index n2, derive the relation.
, where symbols have their usual meaning. vuR
(ii) Explain briefly how the focal length of a convex lens changes with increase in wavelength of incident light.
(iii) What happens to the focal length of convex lens when it is immersed in water? Refractive index of the material of lens is greater than that of water.