Q37 of 104 Page 306

Consider the situation of the previous problem.

(a) Calculate the force needed to keep the sliding wire moving with a constant velocity v.


(b) If the force needed just after t = 0 is F0, find the time at which the force needed will be F0/2.


Formula used:


(a) Magnetic force on a current carrying wire where I = current, l = length of wire, B = magnetic field.


Since l and B are perpendicular to each other, magnetic force F becomes … (i)


Now, from the previous problem, … (ii)


Now, the force needed to keep the sliding wire from moving will be equal to the magnetic force, but in the opposite direction.


Let this force be F’.


Hence, , where F = magnetic force, I = current, L = length of wire, B = magnetic field.


Substituting the value of I from (ii):


=


Hence, force required to keep the wire from sliding = (Ans)


(b) Now, just after time t = 0, the force required to stop the wire from sliding will be … (i) (substituting t = 0), from the previous part of this question.


Now, let the time taken for the required force to be be t = T.


Hence, from the previous question, substituting t = T,


… (ii)


Substituting the value of F0 from (i), we get



⇒


⇒


Time taken for the force to reduce to (Ans)


More from this chapter

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35

Figure shows a wire sliding on two parallel, conducting rails placed at a separation ℓ. A magnetic field B exists in a direction perpendicular to the plane of the rails. What force is necessary to keep the wire moving at a constant velocity v?


 36

Figure shows a long U-shaped wire of width ℓ placed in a perpendicular magnetic field B. A wire of length ℓ is slid on the U-shaped wire with a constant velocity v towards right. The resistance of all the wires is r per unit length. At t = 0, the sliding wire is close to the left edge of the U-shaped wire. Draw an equivalent circuit diagram, showing the induced emf as a battery. Calculate the current in the circuit.


 38

Consider the situation shown in figure. The wire PQ has mass m, resistance r and can slide on the smooth, horizontal parallel rails separated by a distance ℓ. The resistance of the rails is negligible. A uniform magnetic field B exists in the rectangular region and a resistance R connects the rails outside the field region. At t = 0, the wire PQ is pushed towards right with a speed v0. Find

(a) the current in the loop at an instant when the speed of the wire PQ is v,


(b) the acceleration of the wire at this instant,


(c) the velocity v as a function of x and


(d) the maximum distance the wire will move.



 39

A rectangular frame of wire abcd has dimensions 30 cm × 80 cm and a total resistance of 2.0 Ω. It is pulled out of a magnetic field B = 0.020 T by applying a force of 3.2 × 10–6 N (figure). It is found that the frame moves with constant speed. Find

(a) this constant speed,


(b) the emf induced in the loop,


(c) the potential difference between the points a and b and (d) the potential difference between the points c and d.