Phy 1 (14)
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http://www.rpmauryascienceblog.com/
Q.1.
Y
There is a uniform field B = B0 ˆi in the region. Loop PQRS is having a radius R and mass ‘m’ and is circular in shape. The loop is constrained to rotate along the y-axis. It rotates only due to the torque of the magnetic forces acting on it. Calculate its angular speed when it has rotated through an angle 900. Initially, the loop was lying in the x-y plane. The loop is carrying a current I as shown in the figure.
I P
Q X
X R
S
Y
Q.2.
Q.3.
Q.4.
A charged particle is projected in a magnetic field B = (3i + 4j) 10-2 T. The acceleration of the 8 particle is found to be a ( ˆi yˆj ) m/s2. Find the value of y. 3 A small square loop of wires of side is placed inside a large circular r wire of radius R (R >> ). The loops are coplanar and their centres coincide. Find the mutual inductance of the system.
A circular loop of conducting wire of length 0.5 m lies in a magnetic field of 1.0 tesla perpendicular to the plane of the loop. Calculate the tension developed in the wire if the current flowing in the wire is /2 ampere. Also find the direction of current.
dF dF
× ×
× ×
dF
×
dF
× ×
Q.5.
A particle of charge q and mass m is projected perpendicular to a magnetic field B and it is
observed to rotate w.r.t. an axis whose direction is given by the vector 2iˆ 2ˆj 3kˆ , with an angular speed of
magnetic field B . Q.6.
Q.7.
17 rad/s. If the charge to mass ratio (q/m) of the particle is
3 C/kg, find the
A charged particle is projected in a magnetic field B = (3i + 4j) 10-2 T. The acceleration of the 8 particle is found to be a ( ˆi yˆj ) m/s2. Find the value of y. 3
The magnetic field intensity inside a long solenoid is 1 T. If the current per turn of the winding is 1 A, Find the number of turns in one meter.
http://www.rpmauryascienceblog.com/ Q.8.
A solenoid has an inductance of 10 H and a resistance of 2 . It is connected to a 10 V battery. 1 How long will it take for the magnetic energy to reach of its maximum value? 4
Q.9.
Find the magnetic dipole moment of the rectangular loop shown in the figure. Sides, a = 3m, b = 4m and c = 2m current in the loop I = 1 Amp
Y
c I I
X 450 a
Z
Q.10. Three quarters of loops lying in plane xy, yz and zx have radii R1, R2 & R3 respectively. A current I flows through them. Find the magnetic field induced at the origin of coordinates.
b
I
Y
I I R1
R2
X R3 Z
Q.11. A charged particle is projected in a magnetic field B = (3i + 4j) 10-2 T. The acceleration of the 8 particle is found to be a ( ˆi yˆj ) m/s2. Find the value of y. 3
Q.12. A circular loop of radius R = 20 cm is placed in a uniform magnetic field B = 2T in x-y plane as shown in figure. The loop carries a current i = 1.0 A in the direction shown in figure. Find the magnitude of the torque acting on the loop.
y
B B 0
45
x
Q.13. A charged particle is projected in a magnetic field B = (3i + 4j) 10-2 T. The acceleration of the 8 particle is found to be a ( ˆi yˆj ) m/s2. Find the value of y. 3 Q.14. Two circular coils A and B subtend same solid angle at point P lying on the axis of the coils as shown in figure. Smaller coil B is midway between A and P. Both of the coils have same current in the same direction. Find the ratio of magnetic induction at point P due to coils A and B.
A B I
I
d/2
Q.15. A current carrying wire carrying a current of 1 A, lies along the z-axis which is out of the page, while another wire carrying a current of 2 A lies parallel to the first, as shown in the figure. Draw a loop linking both the wires such that the integral:
B.dr
around this loop is (a) zero.
(b) 16 107 S.I. Units in magnitude
P d/2
y z
1A
x
2A
Currents flowing out of the page
http://www.rpmauryascienceblog.com/ Q.16. A current of i flow around a closed path in the circuit which is in the horizontal plane as shown in the figure. The circuit consists of eight alternating areas of radii r1 and r2. Each subtends the same angle at the centre. Find magnetic field produced by this circuit at the centre.
r2
r1
Q.17. A circular loop of radius R = 20 cm is placed in a uniform magnetic field B = 2T in x-y plane as shown in figure. The loop carries a current i = 1.0 A in the direction shown in figure. Find the magnitude of the torque acting on the loop.
y
B B 450 x
Q.18. Find the magnitude and direction of magnetic dipole moment of the loop shown in figure and the torque acting on it , if there exists a uniform magnetic field given by B 0.2i 0.5 j 3k T .
2A z 40 cm 10 cm y
25 cm
S
Q.19. (a) An electron gun G emits electrons of energy 2KeV travelling in the positive x-direction. The electrons are required to hit the spot S where GS = 0.1m, and the line GS makes an angle of 600 with the x-axis, as shown in the figure. A uniform magnetic field B parallel to GS exists in the region outside the electron gun. Find the minimum value of B needed to make the electrons hit S.
Q.20.
x
B
600 G
X
A particle with charge q is projected successively along the x and y axes with same speed v. The force on the particle in these situations are qvB 3ˆj 4kˆ & qvB 3ˆi respectively. Find the unit vector in direction of B .
http://www.rpmauryascienceblog.com/ Q.21. (a) In the adjoining figure there are shown two current carrying wires 1 and 2. Find the magnitudes and directions of the magnetic field B at the points P, Q and R.
20 Amp
30 Amp
10 cm 10 cm P
10 cm
Q 20 cm
X
R Z
1
2
Q.22. A long straight wire AB carries a current I. A conductor of length L is situated at a distance a (one end) from the wire and moving with velocity v in the plane of the wire in the direction, as shown in the figure. Find the induced emf in the conductor.
A
v
I
L a
B
Q.23. The conductor ABCDEF carries a current of 4 A. Find the net magnetic field at the centre O. C
O 3 cm
/2 4A
D
B
6 cm
A
E
F
Q.24. A conductor of length 1m is lying along the y-axis carrying a current 1 Amp. along the +ve Y-axis. A magnetic field ( ˆi ˆj kˆ ) Tesla is existing in the region. Find the magnetic force acting on the wire. Q.25. A current carrying wire carries a current of 1 A, lies along the z-axis which is out of the page, while another wire carrying a current of 2 A lies parallel to the first, as shown in the figure. Draw a loop linking both the wires such that the integral: B.dr around this loop is (a) zero.
(b) 16107 S.I. Units in magnitude
y z
1A
x
2A
Currents flowing out of the page
Q.26. A wire of length 5.0 cm carries a current of 3.0 A; kept in an external uniform magnetic field B of -3 -2 magnitude 10 Wbm . Calculate the magnetic force exerted on the wire, if the wire is inclined at 30 with B .
http://www.rpmauryascienceblog.com/ D
Q.27. A wire ABCDEF (with each side of length L) bent as shown and carrying a current I is placed in a uniform magnetic induction B parallel to the +ve y-direction. Find the magnitude and direction of the force experienced by the wire.
I
Z E
O
C
B
F
Y
A
X
Q.28. A wire of length 5.0 cm carries a current of 3.0 A; kept in an external uniform magnetic field B of -3 -2 magnitude 10 Wbm . Calculate the magnetic force exerted on the wire, if the wire is inclined at 30 with B . i1
Q. 29. In the adjoining diagram, a current-carrying loop pqrs is placed with its sides parallel to a long current-carrying wire. The currents i1 and i2 in the wire and loop are 20 A and 16 A respectively. If a = 15 cm, b = 6 cm and d = 4 cm, what will be the force on current-loop pqrs? What will be the difference in the force, if the current i2 in the loop is clockwise instead of anticlockwise?
q
p
a
i2
s d
r b
Q.30. A particle of specific charge is projected from origin with velocity v (v 0 ˆi v 0kˆ ) in a uniform magnetic field B B0kˆ . Determine the nature of path i.e. circle / helix / cycloid with reason.
Q.31. A coil of radius R in y-z plane is carrying a current I in clockwise as seen from the right side. There is an infinite wire at point B (R, 0, 0) carrying a current I along negative z. Find net magnetic field at point P (R/2, 0, 0).
I
y
R
x
A
Q.32. A uniform magnetic field with a slit system as shown in figure is to be used as a momentum filter for high-energy charged particles. With a field B Tesla, it is found that the filter transmits - particles each of energy 5.3MeV. The magnetic field is increased to 2.3 B Tesla and deuterons are passed into the filter. Find the energy of deuterons transmitted by the filter.
P
z
B
Source
Detector
http://www.rpmauryascienceblog.com/ Q.33. (a) Find the net magnetic field at point P. 2r r
+ P I -
Q.34. The circular and the straight parts of the wire are made of same material but have different diameters. Find the ratio of their diameters if the magnetic field at the centre is zero. All the wires are in the same plane.
I
120
o
I
Q.35. There exists a long conductor along z-axis carrying current of 5A along +ve direction. Find the total torque on the loop in xy-plane as shown in the diagram. Resistance per unit length of the wire forming loop equals 2 /m. Potential difference VBA = 28 volt. Radii ‘a’ = 0.6 m & b = 0.9 m. as shown.
A /3 /3
O
/6
b
a B
Q.36. A charged particle carrying charge q = 10 C moves with velocity v1 = 106 m/s at angle 450 with yaxis in the xy plane & experiences a force F1 = 5 2 mN along the negative z-axis. When the same particle moves with velocity v2 =106 m/s along the z-axis it experiences a force F2 in y direction. Find (a) magnitude and direction of the magnetic field (b) the magnitude of the force F2
Q.37. A uniformly charged disc whose total charge has magnitude q and whose radius is r rotates with constant angular velocity of magnitude . What is the magnetic dipole moment?
R
r
dR
http://www.rpmauryascienceblog.com/ Q.38. Two long parallel wires carry a current I of equal magnitude but flowing in opposite directions. These wires are suspended by four chords of same length ‘’ as shown in the figure. If the mass per unit length of wire is find the value of ‘’.
i
i
Q.39. (a)Infinite length of wire carrying current I is bended as shown in figure. Find magnetic field intensity at P. P
90
0
Q.40. A particle with charge q is projected successively along the x and y axis with same speed v. The force on the particle in these situations are qvB [(-1/2)j + (3/2)k] and qvB (1/2)i respectively. Find the unit vector in direction of B. Q.41. A circular loop of radius R is bent along a diameter and given a shape as shown in the figure. One of the semi circles (KNM) lies in the x-z plane and the other one (KLM) in the y-z plane with their centres at the origin. Current 1 amp. is flowing through each of the semicircles as shown in figure. Find (a) the magnetic moment of the loop (b) torque on the loop due to the external magnetic field B 3i + 6j - 3k about x-axis.
L M
I
N y I
K
x z
Q.42.
B= 1 Tesla
A conductor AB & U – shaped conducting path with resistor R shown is placed in a uniform vertical field of strength 1 tesla. Initially conductor is at rest. The system is released at t = 0. Find the velocity of the rod of mass m as a function of time. Neglect friction. Take m = 1 kg.
R=1 m
= 1m.
3m
Q.43. ABCDA is a square wire frame of mass 4m free to rotate about an axis BC, through which a current I2 flows. Current I1 flows through a straight infinite fixed wire as shown. The wire frame and the straight wire are in the same plane. Find (i) the force on AD &AB due to I1. (ii) the net torque acting on wire frame about BC due to I1.If the wire frame is initially at rest in the position shown , find the time for the frame to rotate by 450.
a
A
B I2 I1 D
a 2a
C
http://www.rpmauryascienceblog.com/ Q.44. Three infinitely long straight conductors are arranged as shown in the figure. Find the intensity of a magnetic field at points A and B.
Y 2I I
R
Q.45.
X Z P
B
Q
A
A particle with charge q is projected successively along the x and y axes with same speed v. The force on the particle in these situations are 1 3 ˆ qvB ˆj k & qvB 1 / 2ˆi respectively. Find the unit vector in direction of B . 2 2
Q.46. A pair of co-axial coils of radius 10 cm, each consisting 100 turns of wire carrying a current 5 ampier in the same direction, are placed at a distance 10 cm apart as shown in the figure. (a) find the magnetic field at the centre X on the axis of the two coils, where AX = BX = 5 cm (b) If a particle of charge q moves with velocity 106 m/s at an angle of 600 with respect to AB at the point X, find the magnetic force on the particle.
I
I v0
R
x
A
B
Q.47. In the figure shown, resistance per unit length of a square loop of side ‘a’ is . Find the current in the loop as a function of time if x varies as x = vt, where v is aconstant. I
v x
Q.48. A loop is formed by two parallel conductors connected by a solenoid with inductance L and a conducting rod of mass m which can freely (without friction) slide over the conductors. The conductors are located in a horizontal plane in uniform vertical magnetic field B. The distance between the conductors is . At the moment t = 0, the rod is imparted an initial velocity v0 directed to the right. (a) Show that rod will oscillate simple harmonically. (b) Find angular frequency of simple harmonic motion. Q.49. The current in the inner coil is I = 2t2. Find the heat developed in the outer coil between t = 0 and t seconds. The resistance of the inner coil is R and take b >> a.
v0 m
b a
x
http://www.rpmauryascienceblog.com/ Q.50. A rectangular wire frame of dimensions (0.25m 2.0 m) and mass 0.5 kg falls from a height 5m above a region occupied by uniform magnetic field of magnetic induction 1 1 T. The resistance of the wire frame is . Find the time 8 taken by the wire frame when it just starts coming out of the magnetic field.
0.25m d
a
a
b
2m
5m
Q.51. It is required to separate isotopes of U236 and U239. They are singly ionised and energised to 3200 eV before entering the magnetic field in a mass spectrograph. In mass spectrograph they are collected separately after completing semicircular path. If they are to be collected in two pouches separated by a distance of 8 cm, calculate the magnetic flux density needed.
17 m
B
236
U
U
239
S
Q.52. A long copper rod 8 cm in diameter has an off-centre cylindrical hole, as shown in the diagram. This conductor carries a current of 900 amps flowing in the direction into the paper. Find (a) the magnitude and direction of magnetic field at the point P. (b) find the expression for magnetic field at any point inside the cavity.
C1 R
r1
C2 r2
Q.53. A particle of mass 1 10-26 kg and charge 1.6 10-19 coulomb travelling with a velocity 6 1.28 10 m/s in + x direction enters a region in which a uniform magnetic field B and electric field E are present such that Ex = Ey = 0, Ez = - 102.4 kv/m and Bx = Bz = 0, By = 8 10-2 wb/m2. The particle enters this region at the origin at time t = 0. Determine the location (x, y and z co-ordinates) of the particle at t = 5 10-6 sec. Q.54. A non-conducting thin disc of radius R charged uniformly over one side with surface density rotates about its axis with an angular velocity . Find: (i) the magnetic induction at the centre of the disc; (ii) the magnetic moment of the disc. Q.55. The region between x = 0 and x = L is filled with uniform, steady magnetic field B0 kˆ . A particle of mass m, positive charge q and velocity v 0 iˆ travels along x-axis and enters the region of magnetic field. Neglect gravity throughout the question.
http://www.rpmauryascienceblog.com/ (a) Find the value of L if the particle emerges from the region of magnetic field with its final velocity at an angle 30° to the initial velocity. (b) Find the final velocity of the particle and the time spent by it in the magnetic field, if the field now extents up to x = 2.1L. Q.56. For an infinitely long conductor of circular area of cross-section of radius R, current density varies as J = 0 (r/R) where r is distance from centre. Parallel to this conductor another thin infinitely long current carrying wire is placed such that the distance between the axis of two conductor is d (d > R) . If on the line joining the axis of these two conductors at a point at distance a from axis of Ist conductor a < R, magnetic field is zero. Find the current in wire. Q.57. Two semi circular loops A and B are joined in such a manner that their planes are at right angles to each other. Their common axis PQ lies along y-axis. Plane of loop A makes an angle of 450 with the y-z plane. Number of turns in both the loops equals to 10. Current in the loops = 5A. Radius or each loop = 1m
A
Q
z
P
y
B
-x
(a) find the vector dipole moment of the system. (b) find torque acting on the system if an external uniform magnetic field B = ( ˆi ˆj kˆ ) Tesla is present at the site. Q.58. A ring of radius R0 is placed parallel to x-y plane with its centre coinciding with z-axis, at a distance z from the origin of coordinates. A uniform magnetic field B acts also along the zaxis. A charged particle of charge q and mass m is projected with velocity v making an angle with the z-axis in the y-z plane from the origin of the coordinates. Find the minimum value of z coordinate for which the charge particle will move just from outside of the ring. (Assuming v to be sufficient for this to happen).
y
v
q m
z
R0
z
x
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