Magnetic Effects of Current and Magnetism
- A 250 - Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 μA and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by 180^° against the torque is : Answer: 4. 9.1 μ J Key idea: work done in rotating a coil from θ=0 to 180^° is W=MB(cos0-cos180)=2MB , with M=NIA . A=2.1×10⁻²×1.25×10⁻²=2.6... 1
- If θ_1 and θ_2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by : Answer: 4. cot²θ=cot²θ₁+cot²θ₂ Key idea: in a vertical plane at angle α to the magnetic meridian, tanθ'=tanθ/cosα , i.e. cotθ'=cotθcosα . Fo... 1
- An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current 'I' along the same direction is shown in Fig. Magnitude of force per unit length on the middle wire 'B' is given by : Answer: 3. μ₀ i²/√(2)π d Key idea: parallel wires carrying current in the same direction attract each other, each pair giving a force per un... 1
- A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be Answer: 1. n²B Field at the centre of a circular coil: B=μ₀ N I/2r . One turn: wire length L=2π r , so B=μ₀ I/2r . n turns from the same wir... 1
- An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57×10^-2 T. If the value of e/m is 1.76×10^11 C/kg, the frequency of revolution of the electron is Answer: 4. 1 GHz An electron in a magnetic field circles with frequency f=eB/2π m=1/2π·e/m· B . f=frac1.76×10¹¹×3.57×10⁻²2×3.14=frac6.28×10⁹... 1
- A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by 60° is W. Now the torque required to keep the magnet in this new position is Answer: 1. sqrt3W Work to rotate a magnet from equilibrium ( θ=0 ) is W=MB(1-cosθ) ; torque at angle θ is τ=MBsinθ . W=MB(1-cos60^°)=MB/2 ,... 1
- A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross - section. The ratio of the magnetic fields B and B', at radial distances a/2 and 2a respectively, from the axis of the wire is : Answer: 3. 1 Key idea: use Ampere's law. Inside the wire, B=μ₀Ir/2π a² ; outside, B=μ₀I/2π r . At r=a/2 : B=μ₀I/4π a . At r=2a : B'=μ₀I/4π a... 1
- A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be : Answer: 1. 2μ₀ Ii/3π Key idea: forces on the two sides parallel to the wire add up; forces on the other two sides cancel. Side nearest the w... 1
- The magnetic susceptibility is negative for : Answer: 1. diamagnetic material only Key idea: only diamagnetic materials get magnetised opposite to the applied field. Diamagnetic: chi sma... 1