The figure shows a conductor of length l = 0.5 m and resistance r = 0.5 ohm sliding without friction at a velocity v = 2 m/s over two conducting parallel rods ab and cd lying in a horizontal plane. A resistance R = 2.5 Ω connects the ends b and c. A vertical uniform magnetic field of induction B = 0.6 T exists over the region.
Determine (i) the current in the circuit, (ii) the force in the direction of motion to be applied to the conductor for

the latter to move with the velocity v and
(iii) the thermal power dissipated by the circuit. Neglect the resistance of the guiding rods ab and cd.

Solution

Given, a conductor and two conducting parallel rods.
Length of conductor, l = 0.5 m
resistance, r = 0.5 ohm
velocity, v = 2 m/s
Resistance of rod, R = 2.5 ohm
Magnetic field, B = 0.6 T

The conductor ef moves with a velocity v perpendicular to a uniform magnetic induction B and hence induces an emf E = Blv.

The resistance of the circuit = (R + r)

(i) Hence, the current in the circuit $= \frac{Blv}{R + r}$
$= \frac{(0.6) (0.5) (2)}{(2.5 + 0.5)} = 0.2 A$

(ii) The power spend in the system
$P = \frac{E^{2}}{R} F . v = \frac{(Blv)^{2}}{(R + r)} F = \frac{B^{2} l^{2} v}{R + r} = \frac{(0.6)^{2}}{3 \times 2} = 0.06 N$
A force of 0.06 N is required to maintain the motion of the conductor
(iii) The power generated $F . v = \frac{(Blv)^{2}}{(R + r)}$

$= 0.06 \times 2 = 0.12 W$

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?