1. A tightly wound 100 turns coil of radius 10 cm carries a current of 7A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as 4π × 10⁻⁷ SI units):

(1).44 mT

(2). 4.4 T

(3). 4.4 mT

(4). 44 T

2. If the galvanometer G does not show any deflection in the circuit shown, the value of R is given by

(1).50 Ω

(2). 100 Ω

(3). 400 Ω

(4). 200 Ω

3. A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The magnetic field at point P for steady current configuration is given by

(1).\(\displaystyle\frac{µ_0i}{4R}\) pointed away from the page

(2). \(\displaystyle\frac{µ_0i}{4R}\) \(\displaystyle[1 - \frac{2}{\pi}]\) pointed away from the page

(3). \(\displaystyle\frac{µ_0i}{4R}\) \(\displaystyle[1 - \frac{2}{\pi}]\) pointed the page

(4). \(\displaystyle\frac{µ_0i}{4R}\) pointed into the page

4. A wire carrying a current I along the positive x-axis has length L. It is kept in a magnetic field \(\vec{B}\) = \(\left( 2\hat{i} + 3\hat{j} - 4\hat{j}\right)\)T. The magnitude of the magnetic force acting on the wire is

(1).\(\sqrt{5}/L\)

(2). \(5/L\)

(3). \(\sqrt{3}/L\)

(4). \(3/IL\)

5. A long straight wire of length 2 m and mass 250 g is suspended horizontally in a uniform horizontal magnetic field of 0.7 T. The amount of current flowing through the wire will be (g = 9.8 ms⁻²):

(1).2.45 A

(2). 2.25 A

(3). 2.75 A

(4). 1.75 A

6. A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron:

(1).will turn towards right of direction of motion

(2). will turn towards left of direction of motion

(3). speed will decrease

(4). speed will increase

7. A closely packed coil having 1000 turns has an average radius of 62.8 cm. If current carried by 62.8 cm the wire of the coil is 1A the value of magnetic field produced at the centre of the coil will be (permeability of free space = 4π × 10⁻⁷ H ∕ m) nearly .

(1).10⁻³ T

(2). 10 ⁻¹ T

(3). 10⁻² T

(4). 10² T

8. The shape of the magnetic field lines due to an infinite long, straight current carrying conductor is :

(1).a plane

(2). a straight line

(3). circular

(4). elliptical

9. Two very long, straight, parallel conductors A and B carry current of 5 A and 10 A respectively and are at a distance of 10 cm from each other. The direction of current in two conductors is same. The force acting per unit length between two conductors is: (µ₀ = 4π × 10⁻⁷ Sl unit)

(1).1 × 10⁻⁴Nm⁻¹ and is repulsive

(2). 2 × 10⁻⁴Nm⁻¹ and is attractive

(3). 2 × 10⁻⁴Nm⁻¹ and is repulsive

(4). 1 × 10⁻⁴Nm⁻¹ and is attractive

10. The magnetic field on the axis of a circular loop of radius 100 cm carrying current I = √2 A, at point 1 m away from the centre of the loop is given by:

(1).6.28 × 10 ⁻⁴ T

(2). 3.14 × 10 ⁻⁷ T

(3). 6.28 × 10 ⁻⁷ T

(4). 3.14 × 10 ⁻⁴ T

11. From Ampere's circuital law for a long straight wire of circular cross section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is

(1).Uniform and remains constant for both the regions.

(2). A linearly increasing function of distance upto the boundary of the wire and then linearly decreasing for the outside region.

(3). A linearly increasing function of distance r upto the boundary of the wire and then decreasing one with \(\frac{1}{r}\) dependence for the outside region.

(4). A linearly decreasing function of distance upto the boundary of the wire and then a linearly increasing one for the outside region.

12. Given below are two statements. Statement I : Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current carrying conductor only. Statement II : Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Id while the later being produced by a vector source, q. In light of above statements choose the most appropriate answer from the options given below

(1).Both Statement I and Statement II are correct

(2). Both Statement I and Statement II are incorrect

(3). Statement I is correct and Statement II is incorrect

(4). Statement I is incorrect and Statement II is correct

13. A thick current carrying cable of radius 'R' carries current 'I' uniformlydistributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by

(1).

(2).

(3).

(4).

14. An infinitely long straight conductor carries a current of 5A as shown. An electron is moving with a speed of 10⁵ m ∕ s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

(1).4 × 10⁻²⁰ N

(2). 8π × 10⁻²⁰ N

(3). 4π × 10⁻²⁰ N

(4). 8 × 10⁻²⁰ N

15. In the product \(\vec{F} = q \left(\vec{v} × \vec{B}\right) = q\vec{V} × \left( B\hat{i} + B\hat{j} + B_0\hat{k}\right)\) For q = 1 and \(\vec{V} = 2\hat{i} + 4\hat{j} + 6\hat{k}\) and \(\vec{F} = 4|hat{i} - 20\hat{j} + 12\hat{k}\) What will be the complete expression for \(\vec{B}\)

(1).\(-8\hat{i} - 8\hat{j} - 6\hat{k}\)

(2). \(-6\hat{i} - 6\hat{j} - 8\hat{k}\)

(3). \(8\hat{i} + 8\hat{j} - 6\hat{k}\)

(4). \(6\hat{i} + 6\hat{j} - 8\hat{k}\)

16. A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is: (µ₀ = 4π × 10⁻⁷T mA⁻¹)

(1).3.14 × 10⁻⁴T

(2). 6.28 × 10⁻⁵T

(3). 3.14 × 10⁻⁵T

(4). 6.28 × 10⁻⁴T

17. A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field, B with the distance, d from the centre of the conductor, is correctly represented by the figure

(1).

(2).

(3).

(4).

18. Ionized hydrogen atoms and α-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths r_H : r_α wil be

(1).1 : 4

(2). 2 : 1

(3). 1 : 2

(4). 4 : 1

19. Two toroids 1 and 2 have total number of turns 200 and 100 respectively with average radii 40cm and 20cm respectively. If they carry same current i, the radio of the magnetic fields along the two loops is

(1).1 : 1

(2). 4 : 1

(3). 2 : 1

(4). 1 : 2

20. A straight conductor carrying current i splits into two parts as shown in the figure. The radius of the circular loop is R. The total magnetic fieldat the centre P at the loop is

(1).\(Zero\)

(2). \(3µ_0 i ∕ 32R\), outward

(3). \(3µ_0 i ∕ 32R\), inward

(4). \(\displaystyle\frac{µ_0i}{2R}\) ,inward

21. A metallic rod of mass per unit length 0.5 kgm⁻¹ is lying horizontally on a smooth inclined plane which makes an angle of \(30^\circ\) with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 T is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is

(1).7.14 A

(2). 5.98 A

(3). 14.76 A

(4). 11.32 A

22. Current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is

(1).40 Ω

(2). 25 Ω

(3). 250 Ω

(4). 500 Ω

23. An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current I along the same direction as shown in figure. Magnitude of force per unit length on the middle wire ‘B’ is given by

(1).\(\displaystyle\frac{2µ_0I^2}{πd}\)

(2). \(\displaystyle\frac{2µ_0I^2}{πd}\)

(3). \(\displaystyle\frac{µ_0I^2}{\sqrt{2}πd}\)

(4). \(\displaystyle\frac{µ_0I^2}{2πd}\)

24. 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 \(\displaystyle\frac{a}{2}\) and \(2a\) respectively, from the axis of the wire is

(1).\(1\)

(2). \(4\)

(3). \(\displaystyle\frac{1}{4}\)

(4). \(\displaystyle\frac{1}{2}\)

25. A square loop ABCD carrying a current is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be

(1).\(\displaystyle\frac{2µ_0I iL}{3π}\)

(2). \(\displaystyle\frac{µ_0I iL}{2π}\)

(3). \(\displaystyle\frac{2µ_0I i}{3π}\)

(4). \(\displaystyle\frac{µ_0I i}{2π}\)

26. 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

(1).nB

(2). n²B

(3). 2nB

(4). 2n²B

27. An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57 × 10⁻²T If the value of e/m is 1.76 × 10¹¹Ckg⁻¹, the frequency of revolution of the electron is

(1).1 GHz

(2). 100 MHz

(3). 62.8 MHz

(4). 6.28 MHz

28. An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude

(1).\(\displaystyle\frac{µ_0n^2e}{r}\)

(2). \(\displaystyle\frac{µ_0ne}{2r}\)

(3). \(\displaystyle\frac{µ_0ne}{2πr}\)

(4). \(Zero\)

29. A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point O is

(1).\(\displaystyle\vec{B} = - \frac{µ_0 I}{4π R} \left(π\hat{i} + 2\hat{k}\right)\)

(2). \(\displaystyle\vec{B} = \frac{µ_0 I}{4π R} \left(π\hat{i} - 2\hat{k}\right)\)

(3). \(\displaystyle\vec{B} = \frac{µ_0 I}{4π R} \left(π\hat{i} + 2\hat{k}\right)\)

(4). \(\displaystyle\vec{B} = - \frac{µ_0 I}{4π R} \left(π\hat{i} - 2\hat{k}\right)\)

30. A proton and an alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be

(1).1.5 MeV

(2). 1 MeV

(3). 4 MeV

(4). 0.5 MeV

31. In an ammeter 0.2% of main current passes through the galvanometer.If resistance of galvanometer is G, the resistance of ammeter will be

(1).\(\displaystyle\frac{1}{499}\)G

(2). \(\displaystyle\frac{499}{500}\)G

(3). \(\displaystyle\frac{1}{500}\)G

(4). \(\displaystyle\frac{500}{499}\)G

32. Two identical long conducting wires AOB and COD are placed at right angle to each other, with one above other such that O is their common point for the two. The wires carry I₁ and I₂ currents, respectively. Point P is lying at distance d from O along a direction perpendicular to the plane containing the wires. The magnetic field at the point P will be

(1).\(\displaystyle\frac{µ_0}{2πd}\left(\frac{I_1}{I_2}\right)\)

(2). \(\displaystyle\frac{µ_0}{2πd}\left(I_1 + I_2\right)\)

(3). \(\displaystyle\frac{µ_0}{2πd}\left(I_1^2 - I_2^2\right)\)

(4). \(\displaystyle\frac{µ_0}{2πd}{\left(I_1^2 + I_2^2\right)}^{1/2}\)

33. A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n(h/e) where n is an integer, h is Planck's constant and e is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be (m is the mass of the electron)

(1).\(\displaystyle \frac{\text{heB}}{2\pi\text{m}}\)

(2). \(\displaystyle \frac{\text{he}}{\pi\text{m}}\)

(3). \(\displaystyle \frac{\text{he}}{2\pi\text{m}}\)

(4). \(\displaystyle \frac{\text{heB}}{\pi\text{m}}\)