Q27 of 91 Page 230

The magnetic field existing in a region is given by


A square loop edge ℓ and carrying a current i, is placed with its edges parallel to the x-y axes. Find the magnitude of the net magnetic force experienced by the loop.



Given-


A square loop with-


Magnetic field,


Length of the edge of a square loop = l



Electric current flowing through it = i



Given in the question that the loop is lies with its edges parallel to the X−Y axes.


Capture.PNG
In the fig, arrow shows the direction of force on different sides of the square.



Magnetic force acting due to presence of current on a small length l given by –




where,


= magnetic field


I = current


= length of the wire


Now,


Force on side AB -



Consider a differential element of length dx at a distance x from the origin along line AB



Force on this small element,



Force on the full length of AB,





Force on AB will be acting downwards.



Similarly, force on CD,



The net force acting vertically will be -





Force on AD,




Force on BC



Then, the net horizontal force




More from this chapter

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25

Figure shows a circular wire-loop of radius a, carrying a current i, placed in a perpendicular magnetic field B.

(a) Consider a small part dl of the wire. Find the force on this part of the wire exerted by the magnetic field.


(b) Find the force of compression in the wire.



 26

Suppose that the radius of cross section of the wire used in the previous problem is r. Find the increase in the radius of the loop if the magnetic field is switched off. The Young modulus of the material of the wire is Y.

 28

A conducting wire of length ℓ, lying normal to a magnetic field B, moves with velocity v as shown in figure.

(a) Find the average magnetic force on a free electron of the wire.


(b) Due to this magnetic force, electrons concentrate at one end resulting in the electric field inside the wire. The redistribution stops when the electric force on the free electrons balances the magnetic force. Find the electric field developed inside the wire when the redistribution stops.


(c) What potential difference is developed between the ends of the wire?



 29

A current i is passed through a silver strip of width d and area of cross section A. The number of free electrons per unit volume is π.

(a) Find the drift velocity v of the electrons.


(b) If a magnetic field B exists in the region as shown in figure, what is the average magnetic force on the free electrons?


(c) Due to the magnetic force, the free electrons get accumulated on one side of the conductor along its length. This produces a transverse electric field in the conductor which opposes the magnetic force on the electrons. Find the magnitude of the electric field which will stop further accumulation of electrons.


(d) What will be the potential difference developed across the width of the conductor due to the electron-accumulation? The appearance of a transvers emf, when a current carrying wire is placed in a magnetic field, is called Hall effect.