Physics

Moving Charges and Magnetism

Question:

A circular current loop of magnetic moment Mis in an arbitrary orientation in an external magnetic field B. The work done to rotate the loop by 30 ° about an axis perpendicular to its plane is
ncert-exemplar-problems-class-12-physics-moving-charges-and-magnetism-9

Answer:

(d)
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Moving Charges and Magnetism

Q 1.

A charged particle would continue to move with a constant velocity in a region wherein,
(a) E = 0,B≠0 (b) E≠0,B≠0
(c) E≠0,B = 0 (d) E = 0, B = 0

Q 2.

Two identical current carrying coaxial loops, carry current I in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as C,
(a) ФBdl =mμ0I
(b) the value of  Ð¤B.dl = ±2μ0I is independent of sense of C
(c) there may be a point on C where, B and dl are perpendicular
(d) B vanishes everywhere on C

Q 3.

The magnetic force depends on v which depends on the inertial frame of reference. Does then the magnetic force differ from inertial frame to frame? Is it reasonable that-the net acceleration has a different value indifferent frames of reference?

Q 4.

A charged particle of charge e and mass m is moving in an electric field E and magnetic field B. Construct dimensionless quantities and quantities of dimension [T]-1  .

Q 5.

An electron and a positron are released from (0, 0, 0) and (0, 0, 1.5R) respectively, in a uniform magnetic field B = B0i, each with an equal momentum of magnitude p = eBR. Under what conditions on the direction of momentum will the orbits be non-intersecting circles?

Q 6.

A multirange current meter can be constructed by using a galvanometer circuit as shown in figure. We want a current meter that can measure 10 mA, 100 mA and 1 mA using a galvanometer of resistance 10 Ω and that produces maximum deflection for current of 1 mA. Find S1  ,S2 and S3 that have to be used.
ncert-exemplar-problems-class-12-physics-moving-charges-and-magnetism-36

Q 7.

An electron enters with a velocity v = v0i into a cubical region (face parallel to coordinate planes) in which there are uniform electric and magnetic fields. The orbit of the electron is found to spiral down inside the cube in a plane parallel to the x-y plane. Suggest a configuration to fields E and B that can lead to it.

Q 8.

A 100 turn rectangular coil ABCD (in X-Y plane) is hung from one arm of a balance (shown in figure). A mass 500 g is added to the other arm to balance the weight of the coil. A current 4.9 A passes through the coil and a constant magnetic field of 0.2 T acting inward (in x-z plane) is switched on such that only arm CD of length 1 cm lies in the field. How much additional mass m must be added to regain the balance?

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Q 9.

Show that a force that does no Work must be a velocity dependent force.

Q 10.

Consider a wire carrying a steady current, I placed in a uniform magnetic field B perpendicular to its length. Consider the charges inside the wire. It is known that magnetic forces do not work. This implies that,
(a) motion of charges inside the conductor is unaffected by B, since they do not absorb energy.
(b) some charges inside the wire move to the surface as a result of B.
(c) if the wire moves under the influence of B, no work is done by the force.
(d) if the wire moves under die influence of B, no work is done by the magnetic force on the ions, assumed fixed within the wire.

Q 11.

Do magnetic forces obey Newton's third law. Verify for two current elements dl1 = dl i located at the origin and dl2 = dl j located at(0, R, 0). Both carry current I.

Q 12.

Two long wires carrying current I1, and I2 are arranged as shown in figure. The one carrying current I1 is along the x-axis. The other carrying current I2 is along a line parallel to the y-axis given by x = 0 and z = d. Find the force exerted at O2 because of the wire along the x-axis.
ncert-exemplar-problems-class-12-physics-moving-charges-and-magnetism-16

Q 13.

Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled.

Q 14.

A current carrying circular loop of radius R is placed in the x-y plane with centre at the origin. Half of the loop with x >0 is now bent so that it now lies in the y-z plane.
(a) The magnitude of magnetic moment now diminishes.
(b) The magnetic moment does not change.
(c) The magnitude ofB at (0,0, z), z>>R increases.
(d) The magnitude ofB at (0,0,z), z>>R is unchanged.

Q 15.

A multirange voltmeter can be constructed by using a galvanometer circuit as shown in figure. We want to construct a voltmeter that can measure 2 V, 20 V and 200 V using a galvanometer of resistance 10 Ω and that produces maximum deflection for current of 1 mA. Find R1, R2 and R3 that have to be used,

ncert-exemplar-problems-class-12-physics-moving-charges-and-magnetism-23

Q 16.

A rectangular conducting loop consists of two wires on two opposite sides of length l joined together by rods of length d. The wires each are of the same material but with cross-sections differing by a factor of 2. The thicker wire has a resistance R and the rods are of low resistance, which in turn are connected to a constant voltage source V0. The loop is placed in a uniform magnetic field B at 45 ° to its plane. Find T, the torque exerted by the magnetic field on the loop about an axis through the centres of rods.

Q 17.

Five long wires A, B, C, D and E, each carrying current I are arranged to form edges of a pentagonal prism as shown in figure. Each carries current out of the plane of paper.
(a) What will be magnetic induction at a point on the axis 0? Axis is at a distance R from each wire.
(b) What will be the field if current in one of the wires (say A) is switched off?
(c) What if current in one of the wire (say A) is reversed?

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Q 18.

In a cyclotron, a charged particle
(a) undergoes acceleration all the time
(b) speeds up between the dees because of the magnetic field
(c) speeds up in a dee
(d) slows down within a dee and speeds up between dees

Q 19.

A cubical region of space is filled with some uniform electric and magnetic fields. An electron enters thq cube across one of its faces with velocity v and a positron enters via opposite face with velocity -v. At this instant,
(a) the electric forces on both the particles cause identical accelerations.
(b) the magnetic forces on both the particles cause equal accelerations.
(c) both particles gain or loose energy at the same rate.
(d) the motion of the Centre of Mass (CM) is determined by B alone.

Q 20.

A long straight wire carrying current of 25 A rests on a table as shown in figure. Another wire PQ of length 1 m, mass 2.5 g carries the same current but in the opposite direction. The wire PQ is free to slide up and down. To what height will PQ rise?
ncert-exemplar-problems-class-12-physics-moving-charges-and-magnetism-25

Q 21.

Biot-Savart law indicates that the moving electrons (velocity v) produce a magnetic field B such that
(a) B is perpendicular to v.
(b) B is parallel to v.
(c) it obeys inverse cube law.
(d) it is along the line joining the electron and point of observation.

Q 22.

A current carrying loop consists of 3 identical quarter circles of radius R, lying in the positive quadrants of the x-y, y-z and z-x planes with their centres at the origin, joined together. Find the direction and magnitude of B at the origin.

Q 23.

An electron is projected with uniform velocity along the axis of a current carrying long solenoid. Which of the following is true?
(a) The electron will be accelerated along the axis
(b) The electron path will be circular about the axis
(c) The electron will experience a force at 45 ° to the axis and hence execute a helical path
(d) The electron will continue to move with uniform velocity along the axis of the solenoid

Q 24.

Two charged particles traverse identical helical paths in a completely oppo-site sense in a uniform magnetic field B = B0k
(a) They have equal z-components of momenta
(b) They must have equal charges
(c) They necessarily represent a particle, anti-particle pair
(d) The charge to mass ratio satisfy
ncert-exemplar-problems-class-12-physics-moving-charges-and-magnetism-1

Q 25.

The gyro-magnetic ratio of an electron in an H-atom, according to Bohr model, is .
(a) independent of which orbit it is in.
(b) negative
(c) positive
(d) increases with the quantum number n.

Q 26.

Consider a circular current-carrying loop of radius R in the x-y plane with centre at origin. Consider the line integral
ncert-exemplar-problems-class-12-physics-moving-charges-and-magnetism-32

Q 27.

A uniform conducting wire of length 12a and resistance R is wound up as a current carrying coil in the shape of (i) an equilateral triangle of side a, (ii) a square of sides a, and (iii) a regular hexagon of sides a. The coil is connected to a voltage source V0. Find the magnetic moment of the coils in each case.

Q 28.

Verify that the cyclotron frequency ω  = eB/m has the correct dimensions of [T]-1       .

Q 29.

A circular current loop of magnetic moment Mis in an arbitrary orientation in an external magnetic field B. The work done to rotate the loop by 30 ° about an axis perpendicular to its plane is
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