Chapter 19

Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field \(\mathbf{B}=B_{0} \hat{\mathbf{k}} . \quad\) [NCERT Exemplar] (a) They have equal z-components of momenta (b) They must have equal charges (c) They necessarily represent a particle-antiparticle pair (d) The charge to mass ratio satisfy : \(\left(\frac{e}{m}\right)_{1}+\left(\frac{e}{m}\right)_{2}=0\)

A current \(i\) flows along the length of an infinitely long, straight, thin- walled pipe. Then (a) the magnetic field at all points inside the pipe is the same, but not zero (b) the magnetic field at any point inside the pipe is zero (c) the magnetic field as zero only on the axis of the pipe (d) the magnetic field at different at different points inside the pipe

A horizontal overhead power line carries a current of 90 A in east to west direction. What are the magnitude and direction of the magnetic field due to the current \(1.5 \mathrm{~m}\) below the line? (a) \(1.2 \times 10^{-5} \mathrm{~T}\), perpendicularly outward to the plane of paper (b) \(1.9 \times 10^{-5} \mathrm{~T}\), perpendicularly outward to the plane of paper (c) \(2.6 \times 10^{-5} \mathrm{~T}\), perpendicularly inward to the plane of paper (d) \(2.6 \times 10^{-5} \mathrm{~T}\), perpendicularly inward to the plane of paper

In a chamber, a uniform magnetic field of \(6.5 \mathrm{G}\) \(\left(1 \mathrm{G}=10^{-4} \mathrm{~T}\right)\) is maintained. An electron is shot into the field with a speed of \(4.8 \times 10^{6} \mathrm{~m} / \mathrm{s}\) normal to the field explain why the path of the electron is a circle. If \(\left(e=1.6 \times 10^{-19} \mathrm{C}, m_{e}=9.1 \times 10^{-31} \mathrm{~kg}\right)\), then obtain the frequency of revolution of the electron in its circular orbit. (a) \(6 \times 10^{6} \mathrm{~Hz}\) (b) \(18.18 \times 10^{6} \mathrm{~Hz}\) (c) \(10.10 \times 10^{6} \mathrm{~Hz}\) (d) \(12.10 \times 10^{6} \mathrm{~Hz}\)

Biot-Savart law indicates that the moving electrons (velocity \(\mathbf{v}\) ) produce a magnetic field \(\mathbf{B}\) such that [NCERT Exemplar] (a) \(\mathrm{B} \perp \mathrm{v}\) (b) \(\mathrm{B} \| \mathrm{v}\) (c) it obeys inverse cube law (d) it is along the line joining the electron and point of observation

Two very long, straight, parallel wires carry steady currents \(i\) and \(-i\) respectively. The distance between the wires is \(d\). At a certain instant of time, a point charge \(q\) is at a point equidistant from the two wires, in the plane of the wires. Its instantaneous magnitude of the force due to the magnetic field acting on the charge at this instant is (a) \(\frac{\mu_{0} i q v}{2 \pi d}\) (b) \(\frac{\mu_{0} i q v}{\pi d}\) (c) \(\frac{2 \mu_{0} i q v}{\pi d}\) (d) zero

A current \((i)\) carrying circular wire of radius \(R\) is placed in a magnetic field \(B\) perpendicular to its plane. The tension \(T\) along the circumference of wire is (a) \(B \bar{R}\) (b) \(2 \pi \mathrm{BiR}\) (c) \(\pi B i R\) (d) \(2 B i R\)

A uniform electric and magnetic fields are produced pointing in the same direction. If an electron is projected with its velocity pointing in the same direction. \(\quad\) [NCERT Exemplar] (a) The electron velocity will decrease in magnitude (b) The electron velocity will increased in magnitude (c) neither (a) nor (b) (d) None of the above

Two long and parallel straight wires \(A\) and \(B\) carrying currents of \(8.0 \mathrm{~A}\) and \(5.0 \mathrm{~A}\) in the same direction are separated by a distance of \(4.0 \mathrm{~cm}\). Estimate the force on a \(10 \mathrm{~cm}\) section of wire \(A ?\) (a) \(1.5 \times 10^{-5} \mathrm{~N}\) (b) \(2 \times 10^{-5} \mathrm{~N}\) (c) \(4 \times 10^{-5} \mathrm{~N}\) (d) \(3.2 \times 10^{-5} \mathrm{~N}\)

A length \(l\) of wire carries a steady current \(i\). It is bent first to form a circular plane coil of one turn. The same length is now bent more sharply to give three loops of smaller radius. The magnetic field at the centre caused by the same current is (a) one-third of its value (b) unaltered (c) three times of its initial value (d) nine times of its initial value

The magnetic field normal to the plane of a wire of \(n\) turns and radius \(r\) which carries a current \(i\) is measured on the axis of the coil at a small distance \(h\) from the centre of the coil. This is smaller than the magnetic field at the centre by the fraction (a) \((2 / 3) r^{2} / h^{2}\) (b) \((3 / 2) r^{2} / h^{2}\) (c) \((2 / 3) h^{2} / r^{2}\) (d) \((3 / 2) h^{2} / r^{2}\)

The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The dipole axis makes an angle of \(11.3^{\circ}\) with the axis of the earth. At mumbai declination is nearly zero. Then \(\quad\) [NCERT Exemplar] (a) the declination varies between \(11.3^{\circ} \mathrm{W}\) to \(11.3^{\circ} \mathrm{E}\) (b) the least declination is \(0^{\circ}\) (c) the plane defined by dipole and the earth axis posses through greenwich (d) declination average over the earth must be always negative

A pulsar is a neutron star having magnetic field at \(10^{12} \mathrm{G}\) at its surface. The maximum magnetic force experienced by an electron moving with velocity \(0.9 c\) is (a) \(43.2 \mathrm{~N}\) (b) \(4.32 \times 10^{-3} \mathrm{~N}\) (c) \(4.32 \times 10^{3} \mathrm{~N}\) (d) zero

An element, \(d l=d x\) \hat{ i } (where \(d x=1 \mathrm{~cm}\) ) is placed at the origin and carries a large current \(i=10 \mathrm{~A}\). What is the magnetic field on the \(y\)-axis at a distance of \(0.5 \mathrm{~m} ?\) (a) \(2 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}\) (b) \(4 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}\) (c) \(-2 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}\) (d) \(-4 \times 10^{-8} \hat{\mathrm{k}} \mathrm{T}\)

A circular coil \(A\) of radius \(r\) carries current \(i\). Another circular coil \(B\) of radius \(2 r\) carries current of \(i\). The magnetic fields at the centres of the circular coils are in the ratio of (a) \(3: 1\) (b) \(4: 1\) (c) \(1: 1\) (d) \(2: 1\)

An electron is shot in steady electric and magnetic fields such that its velocity \(v\), electric field \(E\) and magnetic field \(B\) are mutually perpendicular. The magnitude of \(E\) is \(1 \mathrm{Vcm}^{-1}\) and that of \(B\) is \(2 \mathrm{~T}\). Now if it so happens that the Lorentz (magnetic) force cancels the electrostatic force on the electron, then the velocity of the electron is (a) \(50 \mathrm{~ms}^{-1}\) (b) \(2 \mathrm{cms}^{-1}\) (c) \(0.5 \mathrm{cms}^{-1}\) (d) \(200 \mathrm{cms}^{-1}\)

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. [NCERT Exemplar] (a) The magnitude of magnetic moment now diminishes (b) The magnetic moment does not change (c) The magnitude of \(\mathrm{B}\) at \((0.0 \mathrm{z}), \mathrm{z>}>R\) increases (d) The magnitude of \(\mathrm{B}\) at \((0.0 . z), \mathrm{z}>R\) is unchanged

A rectangular loop carrying current is placed near a long straight fixed wire carrying strong current such that long sides are parallel to wire. If the current in the nearer long side of loop is parallel to current in the wire. Then the loop (a) experiences no force (b) experiences a force towards wire (c) experiences a force away from wire (d) experiences a torque but no force

Two parallel long wires \(A\) and \(B\) carry currents \(i_{1}\) and \(i_{2}\left(

Current \(i_{0}\) is passes through a solenoid of length \(l\) having number of turns \(N\) when it is connected to a DC source. A charged particle with charge \(q\) is projected along the axis of the solenoid with a speed \(v_{0} .\) The velocity of the particle in the solenoid (a) increases (b) decreases (c) remain same (d) becomes zero

An infinitely long wire carrying current \(i\) is along \(Y\)-axis such that its one end is at point \((0, b)\) while the wire extends upto \(\infty .\) The magnitude of magnetic field strength at point \(P(a, 0)\) is (a) \(\frac{\mu_{0} i}{4 \pi a}\left(1+\frac{b}{\sqrt{a^{2}+b^{2}}}\right)\) (b) \(\frac{\mu_{0} i}{4 \pi a}\left(1-\frac{b}{\sqrt{a^{2}+b^{2}}}\right)\) (c) \(\frac{\mu_{0} i}{4 \pi a}\left(1-\frac{a}{\sqrt{a^{2}+b^{2}}}\right)\) (d) \(\frac{\mu_{0} i}{4 \pi a}\left(1+\frac{a}{\sqrt{a^{2}+b^{2}}}\right)\)

An electron having kinetic energy \(E\) is moving in a circular orbit of radius \(R\) perpendicular to a uniform magnetic field induction \(B\). If kinetic energy is doubled and magnetic field induction is tripled, the radius will become (a) \(R \sqrt{9 / 4}\) (b) \(R \sqrt{3 / 2}\) (c) \(R \sqrt{2 / 9}\) (d) \(R \sqrt{4 / 3}\)

Consider the following statements regarding a charged particle in a magnetic field (i) straight with zero velocity, it accelerates in a direction perpendicular to the magnetic field. (ii) while deflecting in the magnetic field, its energy gradually increases. (iii) only the component of magnetic field perpendicular to the direction of motion of the charged particle is effective in deflecting it. (iv) direction of deflecting force on the moving charged particle is perpendicular to its velocity. Of these statements. (a) (ii) and (iii) are correct (b) (iii) and (iv) are correct (c) (i), (iii) and (iv) are correct (d) (i), (ii) and (iii) are correct

An electron is revolving around a proton in a circular path of diameter \(0.1 \mathrm{~nm}\). It produces a magnetic field \(14 \mathrm{~T}\) at a proton. Then the angular speed of the electron is (a) \(8.8 \times 10^{6} \mathrm{rad} \mathrm{s}^{-1}\) (b) \(4.4 \times 10^{16} \mathrm{rad} \mathrm{s}^{-1}\) (c) \(2.2 \times 10^{16} \mathrm{rad} \mathrm{s}^{-1}\) (d) \(1.1 \times 10^{16} \mathrm{rad} \mathrm{s}^{-1}\)

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 \(45^{\circ}\) 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

A thin disc having radius \(r\) and charge \(q\) distributed uniformly over the disc is rotated \(n\) rotations per second about its axis. The magnetic field at the centre of the disc is (a) \(\frac{\mu_{0} q n}{2 r}\) (b) \(\frac{\mu_{0} q n}{r}\) (c) \(\frac{\mu_{0} q n}{4 r}\) (d) \(\frac{3 \mu_{0} q n}{4 r}\)

The torque required to hold a small circular coil of 10 turns, \(2 \times 10^{-4} \mathrm{~m}^{2}\) area and carrying \(0.5\) A current in the middle of a long solenoid of \(10^{3}\) turns \(\mathrm{m}^{-1}\) carrying 3 A current, with its axis perpendicular to the axis of the solenoid, is (a) \(12 \pi \times 10^{-7} \mathrm{Nm}\) (b) \(6 \pi \times 10^{-7} \mathrm{Nm}\) (c) \(4 \pi \times 10^{-7} \mathrm{Nm}\) (d) \(2 \pi \times 10^{-7} \mathrm{Nm}\)

A closely wound solenoid \(80 \mathrm{~cm}\) long has 5 layers of windings of 400 turns each. The diameter of the solenoid is \(1.8 \mathrm{~cm} .\) If the current carried is \(8.0 \mathrm{~A}\), estimate the magnitude of \(B\) inside the solenoid near its centre. \(\quad\) (a) \(1.5 \times 10^{-2} \mathrm{~T}\), opposite to the axis of solenoid (b) \(2.5 \times 10^{-2} \mathrm{~T}\), along the axis of solenoid (c) \(3.5 \times 10^{-2} \mathrm{~T}\), along the axis of solenoid (d) \(1.5 \times 10^{-2} \mathrm{~T}\), opposite to the axis of solenoid

A steady current \(i\) flows in a small square loop of wire of side \(l\) in a horizontal plane. The loop is now folded about its middle such that half of it lies in a vertical plane. Let \(M_{1}\) and \(M_{2}\) respectively denote the magnetic moments due to current loop before and after folding. Then (a) \(M_{2}=0\) (b) \(M_{1}\) and \(M_{2}\) are in the same direction (c) \(M_{1} / M_{2}=\sqrt{2}\) (d) \(M_{1} / M_{2}=1 / \sqrt{2}\)

Let the magnetic field on the earth be modelled by that of a point magnetic dipole at the centre of the earth. The angle of dip at a point the geographical equator (a) is always zero (b) can be zero at specific points (c) can be positive or negative (d) is bounded

A square frame of side \(1 \mathrm{~m}\) carries a current \(i\), produces a magnetic field \(B\) at its centre. The same current is passed through a circular coil having the same perimeter as the square. The magnetic field at the centre of the circular coil is \(B^{\prime}\). The ratio \(B / B^{\prime}\) is (a) \(\frac{8}{\pi^{2}}\) (b) \(\frac{8 \sqrt{2}}{\pi^{2}}\) (c) \(\frac{16}{\pi^{2}}\) (d) \(\frac{16}{\sqrt{2} \pi^{2}}\)

A long straight, solid metal wire of radius \(2 \mathrm{~mm}\) carries a current uniformly distributed over its circular cross-section. The magnetic field induction at a distance \(2 \mathrm{~mm}\) from its axis is \(B\). Then, the magnetic field induction at distance \(1 \mathrm{~mm}\) from axis will be (a) \(B\) (b) \(B_{1} 2\) (c) \(2 \underline{B}\) (d) \(B\)

A current of \(i\) ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is (a) infinite (b) zero (c) \(\frac{\mu_{0} 2 i}{4 \pi r} \mathrm{~T}\) (d) \(\frac{\mu_{0} i}{2 r} \mathrm{~T}\)

A circular current loop of magnetic moment \(M\) is in an arbitrary orientation in an external magnetic field B. The work done to rotate the loop by \(30^{\circ}\) about an axis perpendicular to its plane is \(\quad\) [NCERT Exemplar] (a) \(M B\) (b) \(\sqrt{3} \frac{M B}{2}\) (c) \(\frac{M B}{2}\) (d) zero

Consider a wire carrying a steady current, \(I\) placed in a uniform magnetic field \(\mathbf{B}\) perpendicular to its length. Consider the charges inside the wire. It is known that magnetic forces do no work. This implies that, \(\quad\) [NCERT Exemplar] (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 \(\mathrm{B}\), no work is done by the force (d) if the wire moves under the influence of \(\mathrm{B}\), no work is done by the magnetic force on the ions, assumed fixed within the wire

A deutron of kinetic energy \(50 \mathrm{keV}\) is describing a circular orbit of radius \(0.5 \mathrm{~m}\), is plane perpendicular to magnetic field \(B\). The kinetic energy of proton that describes a circular orbit of radius \(0.5 \mathrm{~m}\) in the same plane with the same magnetic field \(B\), is (a) \(200 \mathrm{keV}\) (b) \(50 \mathrm{keV}\) (c) \(100 \mathrm{keV}\) (d) \(25 \mathrm{keV}\)

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 \(C, \quad\) [NCERT Exemplar] (a) \(\int_{C} \mathrm{~B} \cdot \mathrm{d} \mathrm{l}=m 2 \mu_{0} l\) (b) the value of \(\int_{C} B \cdot d l\) is independent of sense of \(C\) (c) there may be a point on \(\mathrm{C}\) where \(\mathrm{B}\) and \(\mathrm{d}\) are perpendicular. (d) B vanishes everywhere on \(C\)

A proton, a deutron and an \(\alpha\)-particle enter a magnetic field perpendicular to field with same velocity. What is the ratio of the radii of circular paths? (a) \(1: 2: 2\) (b) \(2: 1: 1\) (c) \(1: 1: 2\) (d) \(1: 2: 1\)

A cubical region of space is filled with some uniform electric and magnetic fields. An electron enters the cube across one of its faces with velocity \(\mathbf{v}\) and a positron enters via opposite face with velocity - v. At this instant, \(\quad\) [NCERT Exemplar] (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

A particle of charge \(q\) and mass \(m\) starts moving from the origin under the action of an electric field, \(E=E_{0}\) î and \(B=B_{0}\) î with a velocity, \(v=v_{0} \hat{\mathbf{j}}\). The speed of the particle will becomes \(\frac{\sqrt{5}}{2} v_{0}\) after a time (a) \(\frac{m v_{0}}{q E}\) (b) \(\frac{m v_{0}}{2 q E}\) (c) \(\frac{\sqrt{3} m v_{0}}{2 q E}\) (d) \(\frac{\sqrt{5} m v_{0}}{2 q E}\)

Consider a coaxial cable which consists of a wire of radius \(a\) and outer cylindrical shell of inner and outer radii \(b\) and \(c\) respectively. The inner wire carries a current \(i\) and outershell carries an equal and opposite current. The magnetic field at a distance \(x\) from axis from \(x

A proton, a deutron and an \(\alpha\)-particle with the same kinetic energy enter a region of uniform magnetic field, moving at right angle to \(B\). What is the ratio of the radius of their circular paths? (a) \(1: \sqrt{2}: 1\) (b) \(1: \sqrt{2}: \sqrt{2}\) (c) \(\sqrt{2}: 1: 1\) (d) \(\sqrt{2}: \sqrt{2}: 1\)

A proton of mass \(1.67 \times 10^{-27} \mathrm{~kg}\) and charge \(1.6 \times 10^{-19} \mathrm{C}\) is projected with a speed of \(2 \times 10^{6} \mathrm{~ms}^{-1}\) at an angle of \(60^{\circ}\) to the \(x\)-axis. If a uniform magnetic field of \(0.104 \mathrm{~T}\) is applied along \(y\)-axis, the path of proton is (a) a circle of radius \(=0.2 \mathrm{~m}\) and time period \(=2 \pi \times 10^{-7} \mathrm{~s}\) (b) a circle of radius \(=0.1\) mand time period \(=2 \pi \times 10^{-7}\) s (c) a helix of radius \(0.1 \mathrm{~m}\) and time period \(=2 \pi \times 10^{-7} \mathrm{~s}\) (d) a helix of radius \(0.2 \mathrm{~m}\) and time period \(=2 \pi \times 10^{-7} \mathrm{~s}\)

An electron and a proton enter a magnetic field perpendicularly. Both have same kinetic energy. Which of the following is true ? (a) Trajectory of electron is less curved (b) Trajectory of proton is less curved (c) Both trajectories are equally curved (d) Both more on straight line path

A uniform magnetic field, \(B=B_{0} \hat{\mathbf{j}}\) exists in space. A particle of mass \(m\) and charge, \(q\) is projected towards \(x\)-axis with speed, \(v\) from a point \((a, 0,0)\). The maximum value of \(v\) for which the particle does not hit the \(y z\)-plane is (a) \(\frac{B q a}{m}\) (b) \(\frac{\mathrm{Bq} a}{2 \mathrm{~m}}\) (c) \(\frac{B q}{a m}\) (d) \(\frac{B q}{2 a m}\)

A particle of mass, \(m\) and charge, \(q\) is placed at a rest in a uniform electric field, \(E\) and then released. The kinetic energy attained by the particle after moving a distance, \(y\) is (a) \(q E y^{2}\) (b) \(q E^{2} y\) (c) \(q E y\) (d) \(q^{2} E y\)

Match the following of Column I with Column II. Column I Column II I. Lorentz force A. \(\oint E \cdot \mathrm{d} \mathbf{A}=\frac{q}{\varepsilon_{0}}\) II. Gauss's law B. \(\quad \mathbf{d B}=\frac{\mu_{0}}{4 \pi} \frac{i \mathbf{d} l \times \mathbf{r}}{r^{3}}\) III. Biot-Savart law C. \(\quad \mathbf{F}=q(\mathbf{E}+(\mathbf{v} \times \mathbf{B}))\) IV. Coulomb's Law D. \(\quad F=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}}\)

A beam of protons is moving parallel to a beam of electrons. Both the beams will tend to (a) repel each other (b) come closer (c) move more apart (d) either (b) or (c)

Assertion A force of \(1 \mathrm{~kg}\)-wt acts on \(1 \mathrm{~m}\) long wire carrying 10 A current held at \(90^{\circ}\) to a magnetic field of \(0.98 \mathrm{~T}\). Reason \(F=B i l \sin \theta\)

A wire of length, \(l\) is bent in the form of circular coil of some turns. A current, \(i\) flows through the coil. The coil is placed in a uniform magnetic field, \(B\). The maximum torque on the coil can be (a) \(\frac{i B l^{2}}{2 \pi}\) (b) \(\frac{i B I^{2}}{4 \pi}\) (c) \(\frac{i B l^{2}}{\pi}\) (d) \(\frac{2 i B l^{2}}{\pi}\)