Q22 of 31 Page 170

The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? Is the force attractive or repulsive?

Given:


Current through the wire, I = 300 A


Length of wire, L1 = 70 cm


Length of wire, L2 = 70 cm


Distance between the wires, d = 1.5 cm



We understand that current carrying conductors create magnetic fields which in turn applies force on nearby current carrying conductor(s).


We know that,


…(1)


Where,


F = force applied


�0 = permeability of free space


I = current through the conductors


d = separation between the conductors


Now, putting the values of F, �0, I and d in equation (1)


⇒


⇒ F = 1.2 Nm-1


Hence, the force applied on the wires is 1.2 N per metre. The force is repulsive in nature because the current is carried in the opposite direction.


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20

A magnetic field set up using Helmholtz coils (described in Exercise 4.16) is uniform in a small region and has a magnitude of 0.75 T. In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through 15 kV enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is 9.0 × 105 V m–1, make a simple guess as to what the beam contains. Why is the answer not unique?

 21

A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires.

(a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?


(b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before? (Ignore the mass of the wires.) g = 9.8 m s–2.

 23

A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,

(a) the wire intersects the axis,


(b) the wire is turned from N-S to northeast-northwest direction,


(c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?

 24

A uniform magnetic field of 3000 G is established along the positive z-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. What is the torque on the loop in the different cases shown in Fig. 4.28? What is the force on each case? Which case corresponds to stable equilibrium?