Chapter 19

A square coil of side \(10 \mathrm{~cm}\) consists of 20 turns and carries a current of \(12 \mathrm{~A}\). The coil is suspended vertically and the normal to the plane of the coil makes an angle of \(30^{\circ}\) with the direction of a uniform horizontal magnetic field of magnitude \(0.80 \mathrm{~T}\). What is the magnitude of torque experienced by the coil? (a) \(0.96 \mathrm{~N}-\mathrm{m}\) (b) \(2.06 \mathrm{~N}-\mathrm{m}\) (c) \(0.23 \mathrm{~N}-\mathrm{m}\) (d) \(1.36 \mathrm{~N}-\mathrm{m}\)

Assertion A charged particle moves perpendicular to a magnetic field. Its kinetic energy remains constant, but momentum changes. Reason Force acts on the moving charged particles in the magnetic field.

Two very long straight parallel wires carry currents \(i\) and \(2 i\) in opposite directions. The distance between the wires is \(r\). 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 velocity \(v\) is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is (a) zero (b) \(\frac{3 \mu_{0}}{2 \pi} \frac{i q v}{r}\) (c) \(\frac{\mu_{0}}{\pi} \frac{i q v}{r}\) (d) \(\frac{\mu_{0}}{2 \pi} \frac{i q v}{r}\)

A metal wire of mass \(m\) slides without friction on two rails placed at a distance \(l\) apart. The track lies in a uniform vertical magnetic field \(B\). A constant current \(i\) flows along the rails across the wire and brack down the other rail. The acceleration of the wire is (a) \(\frac{B m i}{l}\) (b) \(\mathrm{mBi} l\) (c) \(\frac{B i l}{m}\) (d) \(\frac{\mathrm{mil}}{B}\)

Assertion Out of galvanometer, ammeter and voltmeter, resistance of ammeter is lowest and resistance of voltmeter is highest. Reason An ammeter is connected in series and a voltmeter is connected in parallel, in a circuit.

A moving coil galvanometer gives full scale deflection, when a current of \(0.005 \mathrm{~A}\) is passed through its coil. It is converted into a voltmeter reading upto \(5 \mathrm{~V}\) by using an external resistance of \(975 \Omega\). What is the resistance of the galvanometer coil? (a) \(30 \Omega\) (b) \(25 \Omega\) (c) \(50 \Omega\) (d) \(40 \Omega\)

A charge \(Q\) is uniformly distributed over the surface of non-conducting disc of radius \(R\). The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity \(\omega .\) As a result of this rotation a magnetic field of induction \(B\) is obtained at the centre of the disc. If we deep both the amount of charge placed on the disc and its angular velocity to be constant and vary that radius

A voltmeter has resistance of \(2000 \Omega\) and it can measure upto \(2 \mathrm{~V}\). If we want to increase its range by \(8 \mathrm{~V}\), then required resistance in series will be (a) \(4000 \Omega\) (b) \(6000 \Omega\) (c) \(7000 \Omega\) (d) \(8000 \Omega\)

A galvanometer of resistance \(100 \Omega\) gives a full scale deflection for a current of \(10^{-5} \mathrm{~A} .\) To convert it into a ammeter capable of measuring upto \(1 \mathrm{~A}\), we should connect a resistance of (a) \(1 \Omega\) in parallel (b) \(10^{-3} \Omega\) in parallel (c) \(10^{5} \Omega\) in series (d) \(100 \Omega\) in series

A current \(I\) flows in an infinitely long wire with cross-section in the form of a semicircular ring of radius \(R\). The magnitude of the magnetic induction along its axis is (a) \(\frac{\mu_{0} I}{\pi^{2} R}\) (b) \(\frac{\mu_{0} I}{2 \pi^{2} R}\) (c) \(\frac{\mu_{0} I}{2 \pi R}\) (d) \(\frac{\mu_{0} l}{4 \pi R}\)

A microammeter has a resistance of \(100 \Omega\) and full scale range of \(50 \mu \mathrm{A} .\) It can be used as a voltmeter or as a higher range ammeter provided a resistance is added to it. Pick the correct range and resistance combinations (a) \(50 \mathrm{~V}\) range with \(10 \mathrm{k} \Omega\) resistance in series (b) \(10 \mathrm{~V}\) range with \(200 \mathrm{k} \Omega\) resistance in series (c) \(10 \mathrm{~mA}\) range with \(1 \Omega\) resistance in parallel (d) \(10 \mathrm{~mA}\) range with \(0.1 \Omega\) resistance in parallel

An ammeter has resistance \(R_{0}\) and range \(I\). What resistance should be connected in parallel with it to increase its range by \(n I\) ? (a) \(R_{0} /(n-1)\) (b) \(R_{0} /(n+1)\) (c) \(R_{0} / n\) (d) None of these

A charge particle is moving along a magnetic field line. The magnetic force on the particle is [DCE 2009] (a) along its velocity (b) opposite to its velocity (c) perpendicular to its velocity (d) zero

Magnetic field intensity \(H\) at the centre of circular loop of radius \(r\) carrying current \(i\) emu is [WB JEE 2009] (a) \(\frac{r}{i}\) oersted (b) \(\frac{2 \pi i}{r}\) oersted (c) \(\frac{i}{2 \pi r}\) oersted (d) \(\frac{2 \pi r}{i}\) oersted

Which of the following relations represent Biot-Savart's law ? (a) \(\mathrm{dB}=\frac{\mu_{0}}{4 \pi} \frac{i d l}{r} \hat{\mathbf{r}}\) (b) \(\mathrm{dB}=\frac{\mu_{0}}{4 \pi} \frac{i d l}{r^{2}} \mathrm{r}\) (c) \(\mathrm{dB}=\frac{\mu_{0}}{4 \pi} \frac{i \mathrm{~d} \mathrm{l} \times \mathrm{r}}{r^{3}}\) (d) \(\mathrm{dB}=\frac{\mu_{0}}{4 \pi} \frac{i \mathrm{dl}}{r^{4}} \hat{\mathrm{r}}\)

The resistance of the shunt required to allow \(2 \%\) of the main current through the galvanometer of \mathrm{\\{} r e s i s t a n c e ~ \(49 \Omega\) is \(\quad\) [Kerala CET 2008] (a) \(1 \Omega\) (b) \(2 \Omega\) (c) \(0.2 \Omega\) (d) \(0.1 \Omega\) (e) 0010

Oscillating frequency of a cyclotron is \(120 \mathrm{MHz}\). If the radius of its dees is \(0.5 \mathrm{~m}\), the kinetic energy of a proton, which is accelerated by the cyclotron is [Kerala CET 2008] (a) \(10.2 \mathrm{MeV}\) (b) \(2.55 \mathrm{MeV}\) (c) \(20.4 \mathrm{MeV}\) (d) \(5.1 \mathrm{MeV}\) (e) \(21.6 \mathrm{MeV}\)

Two particles of equal charge after being accelerated through the same potential difference enter a uniform transverse magnetic field and describe circular paths of radii \(R_{1}\) and \(R_{2}\) respectively. Then the ratio of their masses \(\left(M_{1} / M_{2}\right)\) is \(\quad\) [Kerala CET 2008] (a) \(R_{1} \overline{/} R_{2}\) (b) \(\left(R_{1} / R_{2}\right)^{2}\) (c) \(\left(R_{2} / R_{1}\right)\) (d) \(\left(R_{2} / R_{1}\right)^{2}\) (e) None of these

A galvanometer of resistance \(50 \Omega\) is connected to a battery of \(3 \mathrm{~V}\) along with a resistance of \(2950 \Omega\) in series. A full scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be \(\quad\) [Kerala CET 2008] (a) \(6050 \Omega\) (b) \(4450 \Omega\) (c) \(5050 \Omega\) (d) \(5550 \Omega\) (e) \(5578 \Omega\)

A circular coil of 5 turns and of \(10 \mathrm{~cm}\) mean diameter is connected to a voltage source. If the resistance of the coil is \(10 \mathrm{~W}\), the voltage of the source so as to nullify the horizontal component of earth's magnetic field of \(30 \mathrm{~A}\) turn \(\mathrm{m}^{-1}\) at the centre of the coil should be \(\quad\) [Kerala CET 2007] (a) \(6 \mathrm{~V}\), plane of the coil normal to the magnetic meridian (b) \(2 \mathrm{~V}\), plane of coil normal to the magnetic meridian (c) \(2 \mathrm{~V}\), plane of the coil along the magnetic meridian (d) \(4 \mathrm{~V}\), plane of the coil normal to magnetic meridian

A conducting rod of \(1 \mathrm{~m}\) length and \(1 \mathrm{~kg}\) mass is suspended by two vertical wires through the ends. An external magnetic fields of \(2 \mathrm{~T}\) is applied normal to the rod. Now the current to be passed through the rod so as to make the tension in the wires zero is (Take \(\left.g=10 \mathrm{~ms}^{-2}\right) \quad[\) Kerala CET 2007] (a) \(0.5 \mathrm{~A}\) (b) \(15 \mathrm{~A}\) (c) \(5 \mathrm{~A}\) (d) \(1.5 \mathrm{~A}\) (e) \(15 \mathrm{~A}\)

A galvanometer of resistance \(20 \Omega\) shown deflection of 10 divisions. When a current of \(1 \mathrm{~mA}\) is passed through it. If a shunt of \(4 \Omega\) is connected and there are 50 divisions on the scale, the range of the galvanometer is [Kerala CET 2007] (a) \(1 \mathrm{~A}\) (b) \(3 \mathrm{~A}\) (c) \(10 \mathrm{~mA}\) (d) \(30 \mathrm{~mA}\) (e) \(11 \mathrm{~mA}\)

Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius \(R\). with constant speed \(v\). The time period of the motion (a) depends on both \(R\) and \(v\) (b) is independent of both \(R\) and \(v\) (c) depends on \(R\) and not on \(\mathrm{V}\) (d) depends on \(v\) and not on \(R\) (e) None of these

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential \(V\) and then made to describe semicircular paths of radius \(R\) using a magnetic field B. If \(V\) and \(B\) are kept constant, the ratio \(\left(\frac{\text { charge on the ion }}{\text { mass of the ion }}\right)\) will be proportional to (a) \(1 / R^{2}\) (b) \(R^{2}\) (c) \(R\) (d) \(1 / R\) (e) \(R^{-3}\)

A solenoid of \(0.4 \mathrm{~m}\) length with 500 turns carries a current of 3 A. A coil of 10 turns and of radius \(0.01 \mathrm{~m}\) carries a current of \(0.4 \mathrm{~A}\). The torque required to hold the coil with its axis at right angles to that of solenoid in the middle point of it is \(\quad\) [Kerala CET 2006] (a) \(6 \pi^{2} \times 10^{-7} \mathrm{Nm}\) (b) \(3 \pi^{2} \times 10^{-7} \mathrm{Nm}\) (c) \(9 \pi^{2} \times 10^{-7} \mathrm{Nm}\) (d) \(12 \pi^{2} \times 10^{-7} \mathrm{Nm}\) (e) \(15 \pi^{2} \times 10^{-7} \mathrm{Nm}\)

A galvanometer coil has a resistance of \(15 \Omega\) and gives full scale deflection for a current of \(5 \mathrm{~mA}\). To convert it to an ammeter of range 0 to \(6 \mathrm{~A}\) [Karnataka CET 2006] (a) \(10 \mathrm{~m} \Omega\) resistance is to be connected in parallel to the galvanometer (b) \(10 \mathrm{~m} \Omega\) resistance is to be connected in series with the galvanometer (c) \(0.1 \Omega\) resistance is to be connected in parallel to the galvanometer (d) \(0.1 \Omega\) resistance is to be connected in series with the galvanometer

A long solenoid has 200 turns per \(\mathrm{cm}\) and carries a current \(i .\) The magnetic field at its centre is \(6.28 \times 10^{-2} \mathrm{Wbm}^{-2} .\) Another along solenoid has 100 turns per \(\mathrm{cm}\) and it carries a current \(i / 3 .\) The value of the magnetic field at its centre [AIEEE 2006] (a) \(1.05 \times 10^{-4} \mathrm{~Wb} \mathrm{~m}^{-2}\) (b) \(1.05 \times 10^{-2} \mathrm{~Wb} \mathrm{~m}^{-2}\) (c) \(1.05 \times 10^{-5} \mathrm{~Wb} \mathrm{~m}^{-2}\) (d) \(1.05 \times 10^{-3} \mathrm{~Wb} \mathrm{~m}^{-2}\)

Two insulating plates are both uniformly charged in such a way that the potential difference between them is \(V_{2}-V_{1}=20 \mathrm{~V}\) (i.e, plate 2 is at a higher potential). The plates are separated by \(d=0.1 \mathrm{~m}\) and can be treated as infinitely large. An electron is released from rest on the inner surface of plate \(1 .\) What is its speed when it hits plate 2 ? [AIEEE 2006] (a) \(32 \times 10^{-19} \mathrm{~ms}^{-1}\) (b) \(2.65 \times 10^{6} \mathrm{~ms}^{-1}\) (c) \(7.02 \times 10^{12} \mathrm{~ms}^{-1}\) (d) \(1.87 \times 10^{6} \mathrm{~ms}^{-1}\)

Two long parallel wires \(P\) and \(Q\) are both perpendicular to the plane of the paper with distance \(5 \mathrm{~m}\) between them. If \(P\) and \(Q\) carry current of \(2.5 \mathrm{~A}\) and 5 A respectively in the same direction, then the magnetic field at a point half way between the wires is (a) \(\frac{\sqrt{3} \mu_{0}}{2 \pi}\) (b) \(\frac{\mu_{0}}{\pi}\) (c) \(\frac{3 \mu_{0}}{2 \pi}\) (d) \(\frac{\mu_{0}}{2 \pi}\)

A straight conductor of length \(l\) carrying a current \(i\), is bent in the form of a semi-circle. The magnetic field in tesla at the centre of the semi-circle is [Kerala CET 2005] (a) \(\frac{\pi^{2} i}{l} \times 10^{-7}\) (b) \(\frac{i \pi}{l} \times 10^{-7}\) (c) \(\frac{\pi i}{I^{2}} \times 10^{-7}\) (d) \(\frac{\pi^{2}}{l} \times 10^{-7}\) (e) None of the above