Important questions of Moving charges and magnetism
Q.1 A wire placed along the north south direction carries a current of 8A from south to north. Find the magnetic field due to a 1 cm piece of wire at a point 200 cm north east from the piece. Ans 1.41 x 10^-9 Inward
Q.2 State Biot-Savart law. Derive an expression for magnetic field at the centre of a circular coil of n- turns carrying current I .
Q.3 A long straight wire carries a current of 35A. What is the magnitude of the field B at a point 20 cm from the wire? Ans. 3.5 x 10^-5 T
Q.4 A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire. Ans. 4 x 10^-5 T, vertically upward
Q.5 A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line? Ans. 1.2 x10^-5 T , towards south.
Q.6 A circular coil having hundred tonnes of wire, of radius 20 cm each, lies in the XY plane with its centre at the origin of coordinates. Find the magnetic field, at the point (0,0,20 root3) cm , when this coil carries a current of 2/ π A. Ans. 25 microT.
Q.7 Find the magnetic field at the centre of each coil if I = 1/π R=25 cm.( Two coils of radius R at distance R root 3). Ans. 0.7 micro T
Q.8 Use Ampere’s Circuital law to find magnetic field due to long straight infinite wire.
Q.9 Find magnetic field due to hollow cylindrical wire using Ampere’s Circuital law.
Q.10 Find Magnetic field due to solid cylindrical wire.
Q.11 A solenoid of length 0.5m has a radius of 1 cm and is made up of 500 turns. It carries a current of 5 A . What is the magnitude of the magnetic field inside the solenoid? Ans .6.28 x 10^-3 T
Q.12 The magnetic field at the centre of a 50cm long solenoid is 4 π x 10^-2 T when a current of 8.0 A flows through it. What is the number of turns in the solenoid. Ans. 6250 turns
Q.13 A toroid has a core of inner radius 20cm and outer radius 22cm around which 4200 turns of wire current is 10A, what is the magnetic field i) inside the core of toroid ii) outside iii) in empty space surrounded by toroid. Ans. 4 x 10^-2 T
Q.14 A coil wrapped around a toroid has inner radius of 20cm and outer radius of 25 cm. If the maximum field inside Toroid is 9.6 mT. Find the magnitude of magnetic field inside the Toroid. Ans. 7.68 mT.
Q.15 An electron is moving northwards with a velocity of 10^7 m/s in a magnetic field of 3T, directed eastwards. Calculate the instantaneous force on the electron. Ans. 4.8 x 10^-12 , outwards.
Q.16 A charged particle of mass 5mg and charge q= +2 micro C has velocity v= 2i -3j + 4k. Find out the magnetic force and its acceleration at this instant due to magnetic field B = 3j -2k . V and B are in m/s and wb/ m², respectively. Ans. F= 2 x 10-6 ( -6i+ 4j +6k) .
Q.17 The magnetic force acting on a positive charge of 1.5 micro C in a magnetic field B =( 2j + 4k)T is F = (6k-12j)N. The velocity of the particle is?
A) 2 x 10^6 i m/s. B) (2i + 4j +2k) x 10^6 m/s. C) (2i+j+2k) x 10^6m/s D) (2i+ 2j+k)x 10^6m/s. (More than one correct) Ans. A & C
Q.18 A charged particle is projected in a Magnetic field of (5i -2j) T. If the acceleration of the particle is found to be (xi+ 5j) m/s² Find x. Ans. 2
Q.19 Find the force on a charge +1microC due to long straight wire at a distance 0.2m moving with 10^6m/s. Wire carries a current of 4A. Ans. 4 microN towards the wire
Question on helical
Q.21 A proton is shot with a speed 5 x 10^6 m/s at an angle of 37° with the x-axis. A uniform magnetic field B = 0.30 T exists along the X - axis. Show that path of the proton is helix . Find radius and pitch of the helix. Ans. 0.1 m, 8 π/ 30 m
Q. 22 A particle with charge ‘q’ and mass m moves with velocity v= 3i+4j m/s in a magnetic field B = 10i T. Find its radius and pitch. Ans. 2m/5q, 3 π m/ 5q
Q.23 An electron accelerated by a potential difference 4.5 kV moves in a uniform magnetic field at an angle 60° to the field whose magnitude is 91 mT. Find the pitch of helical trajectory of electron. Ans. 0.785 cm
Q.24 A velocity selector has E = 2500N/C directed vertically upwards and a constant B directed inwards. A positive charge travelling east at 6 x 10^3 m/s passes undeflected through it. When another charge particle with q= 4x 10^-12 C enters velocity selector travelling east the net force on it is 2 x 10^-9 N. Find the speed of this particle. Ans. 4.8 x 10^3 m/s
Q.25 The square loop is carrying a steady current I and the magnitude of the magnetic dipole moment is M. If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of a circular loop will be? Ans. 4/ π
Q.26 A circular coil of 20 turns and radius 10 cm carries a current of 5 A. It is placed in a uniform magnetic field of 0.10 T. Find the torque acting on the coil when the magnetic field is applied a) normal to the plane of the coil b) in the plane of the coil. Also find out the total force acting on the coil. 0, 0.314 Nm.
Q.27 The maximum torque acting on a coil of effective area 0.04 m² is 4×10 to the power -2 N meter. When the current in it is 100 microA find magnetic field. Ans. 10^4 T
Q.28 A current loop is kept in a uniform magnetic field such that it experiences half of the maximum torque find angle between B and M. Ans. 30°
Q.29 A rectangular coil of area 100 cm² and consisting of 100 turns is suspended in a magnetic field of 5×10^-2 T. What current should be made to pass through it in order to keep equilibrium at an angle of 45° with the field?Given that torsion constant of the suspension fibre is 10^-8 Newton metre per degree. Ans. 9micro A
Q.30 The coil of a pivoted- type galvanometer has 50 turns and encloses an area of 6 m², the magnetic field in the region in which the coil swings is 0.01 T and is radial. The torsional constant of the hairspring is 1.0 x 10^-8 Newton metre per degree find the angular deflection of the coil for a current of 10^-7A. Ans 30°
Q.31 if the current sensitivity of a moving coil galvanometer is increased by 20%, its resistance also increases by 1.5 times. How will the voltage sensitivity be affected? 20%
Q.32 In a chamber, a uniform magnetic field of 6.5 G is maintained. An electron is shot into the field with a speed of 4.8×10^6 m/s normal to the field. Explain why the path of the electron is a circle determine the radius of the circular orbit. Ans 4.2 cm
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