1. The starting idea behind magnetic effects of currents is that they are closely connected with ______.
ⓐ. charges only when they are at rest
ⓑ. neutral bodies kept in vacuum
ⓒ. gravitational attraction between masses
ⓓ. moving charges and electric currents
Correct Answer: moving charges and electric currents
Explanation: Magnetic effects in current-carrying systems arise mainly from charges in motion and from electric currents. An electric current is a directed motion of charges, so it can produce a magnetic field around the conductor. A charge kept at rest may produce an electric field, but it is not the starting source of magnetic effects in current magnetism. This is why a current-carrying wire can deflect a compass needle placed nearby. The key starting contrast is that electrostatics begins with charges at rest, while magnetism here begins with moving charges.
2. A compass needle is placed near a straight wire connected to a battery. When current flows in the wire, the compass needle deflects. This observation mainly shows that a current-carrying wire produces
ⓐ. only an electric field along the wire
ⓑ. no field outside the wire
ⓒ. a magnetic field around the wire
ⓓ. a gravitational field strong enough to rotate the needle
Correct Answer: a magnetic field around the wire
Explanation: A compass needle is a small magnetic system, so its deflection indicates the presence of a magnetic field. When current flows through a straight wire, moving charges in the wire create a magnetic field in the surrounding space. The deflection is not explained by gravitational force because gravitational effects between ordinary laboratory objects are too weak and do not align a compass needle this way. It is also not merely an electric field effect, because the compass responds to magnetic direction. The observation connects electric current with magnetism in a direct and visible way.
3. Magnetic field \(\vec{B}\) is best described as
ⓐ. a vector quantity having both magnitude and direction
ⓑ. a scalar quantity measured only by its magnitude
ⓒ. a scalar quantity that always acts along current
ⓓ. a vector quantity that exists only inside a magnet
Correct Answer: a vector quantity having both magnitude and direction
Explanation: Magnetic field is written as \(\vec{B}\), and the arrow notation indicates that it is a vector quantity. A magnetic field at a point has a magnitude as well as a direction, and both are needed to predict magnetic force or compass orientation. It does not exist only inside a magnet; magnetic fields are also produced around current-carrying conductors. Treating \(\vec{B}\) as a scalar would lose direction information, which is essential in magnetic-force analysis. Direction rules become meaningful only because \(\vec{B}\), velocity \(\vec{v}\), and force \(\vec{F}\) are vector quantities.
4. The magnetic field near a current-carrying conductor is different from an electrostatic field of a stationary charge because the magnetic effect is linked most directly with
ⓐ. mass at rest
ⓑ. temperature difference
ⓒ. charge in motion
ⓓ. pressure difference
Correct Answer: charge in motion
Explanation: A stationary charge is associated with an electric field, but magnetic effects are tied to moving charges. In a current-carrying conductor, charges drift through the wire and produce a magnetic field around it. This does not mean a charge loses its electric nature when it moves; rather, motion adds the magnetic aspect. The comparison helps separate electrostatic effects from magnetic effects in the basic comparison. A current is not just charge present in a wire, but charge moving with a definite average drift.
5. Consider the following examples:
I. Deflection of a compass near a current-carrying wire
II. Rotation of the coil in an electric motor
III. Change in weight of a body on a balance
IV. Deflection in a moving-coil galvanometer
The examples most directly connected with magnetic effects of currents are
ⓐ. I, II, and III only
ⓑ. I, II, and IV only
ⓒ. I and IV only
ⓓ. II, III, and IV only
Correct Answer: I, II, and IV only
Explanation: A compass near a current-carrying wire deflects because the current produces a magnetic field. An electric motor uses force or torque on a current-carrying coil in a magnetic field to produce rotation. A moving-coil galvanometer also depends on torque on a current-carrying coil in a magnetic field. The change in weight of a body on a balance belongs to gravitation or mechanics, not to magnetic effects of moving charges. The listed magnetic examples all involve current, magnetic field, or force on a current-carrying conductor.
6. A loudspeaker is often mentioned with motors and galvanometers because its basic working also involves
ⓐ. magnetic force on a current-carrying coil
ⓑ. electrostatic force between two fixed charges only
ⓒ. heating of a conductor without magnetic interaction
ⓓ. reflection of sound from a rigid wall
Correct Answer: magnetic force on a current-carrying coil
Explanation: A loudspeaker uses a current-carrying coil placed in a magnetic field. When the current changes, the magnetic force on the coil changes, causing motion that produces sound vibrations. The detailed construction is less important than the shared force principle. It belongs with motors and galvanometers because all involve current interacting with a magnetic field. The physical link is force due to magnetism, not sound reflection or only heating of a wire.
7. Study the table and identify the row that gives the best magnetic-effect orientation.
| Row | Situation | Main magnetic idea |
|---|
| P | Current in a straight wire | Magnetic field is produced around the wire |
| Q | Coil in an electric motor | Current in magnetic field can experience torque |
| R | Compass near current | Compass can detect magnetic field direction |
| S | Stone falling freely | Magnetic field is produced by its weight |
Which row does not fit these magnetic-effect examples?
ⓐ. Row P
ⓑ. Row Q
ⓒ. Row R
ⓓ. Row S
Correct Answer: Row S
Explanation: Rows P, Q, and R are all connected with magnetic effects of currents or magnetic field direction. A current in a straight wire produces a magnetic field around it, and a compass can respond to such a field. A motor coil experiences a magnetic torque when current flows through it in a magnetic field. A stone falling freely is a mechanics example involving gravitational force, not a magnetic effect produced by its weight. Magnetic field production is not caused simply by weight; in current magnetism it is linked mainly with currents and moving charges.
8. A student claims that every force on a charge must be electric because charge is an electrical property. The claim misses the fact that
ⓐ. magnetic force can act on a moving charge
ⓑ. a moving charge loses its electric field
ⓒ. magnetic fields act only on neutral bodies
ⓓ. electric force requires charge motion
Correct Answer: magnetic force can act on a moving charge
Explanation: A charge can experience electric force due to an electric field, but a moving charge can also experience magnetic force in a magnetic field. The basic idea shows that motion of charge introduces magnetic effects. The claim is too narrow because it treats charge only from the electrostatic viewpoint. Magnetic force depends on motion and field direction, not merely on the existence of charge. A moving charged particle is therefore a bridge between electric ideas and magnetic-force ideas.
9. Match the quantities with their common symbols.
| Quantity | Symbol |
|---|
| P. Charge | 1. \(\vec{B}\) |
| Q. Velocity | 2. \(q\) |
| R. Magnetic field | 3. \(\vec{v}\) |
| S. Current | 4. \(I\) |
ⓐ. P-3, Q-2, R-1, S-4
ⓑ. P-2, Q-1, R-3, S-4
ⓒ. P-4, Q-3, R-1, S-2
ⓓ. P-2, Q-3, R-1, S-4
Correct Answer: P-2, Q-3, R-1, S-4
Explanation: Charge is commonly denoted by \(q\), while velocity is a vector and is written as \(\vec{v}\). Magnetic field is also a vector, so it is written as \(\vec{B}\). Electric current is denoted by \(I\), and in ordinary circuit notation it is treated as a scalar with an assigned conventional direction. The arrows over \(\vec{v}\) and \(\vec{B}\) are not decoration; they show that direction must be considered in magnetic-force problems. Confusing \(I\) with \(q\) would mix up the flow of charge with the amount of charge itself.
10. The SI unit of magnetic field \(\vec{B}\) is
ⓐ. \(\text{N}\)
ⓑ. \(\text{T}\)
ⓒ. \(\text{C}\)
ⓓ. \(\text{A}\)
Correct Answer: \(\text{T}\)
Explanation: The SI unit of magnetic field is tesla, written as \(\text{T}\). The unit \(\text{N}\) is the unit of force, \(\text{C}\) is the unit of charge, and \(\text{A}\) is the unit of electric current. Magnetic field must have its own unit because it appears in magnetic-force relations involving charge, velocity, current, or conductor length. One useful relation is \(1\,\text{T}=1\,\text{N A}^{-1}\text{m}^{-1}\), which comes from force on a current-carrying conductor. This relation also shows why tesla is connected to force, current, and length together.
11. The unit relation \(1\,\text{T}=1\,\text{N A}^{-1}\text{m}^{-1}\) can be understood most directly from the force relation on a straight current-carrying conductor. In that relation, magnetic field is force per
ⓐ. unit charge and unit speed
ⓑ. unit current and unit length
ⓒ. unit mass and unit acceleration
ⓓ. unit voltage and unit resistance
Correct Answer: unit current and unit length
Explanation: For a straight conductor of length \(l\) carrying current \(I\) in a magnetic field, the magnetic force magnitude is \(F=IlB\sin\theta\). When the conductor is perpendicular to the field, \(\theta=90^\circ\) and \(\sin\theta=1\), so \(B=\frac{F}{Il}\). This gives the unit \(1\,\text{T}=1\,\text{N A}^{-1}\text{m}^{-1}\). The condition of perpendicular arrangement matters because the full relation contains the angle factor. The unit does not come from charge alone; it comes from how magnetic field produces force on a current-carrying length.
12. A second unit form of tesla is \(1\,\text{T}=1\,\text{N s C}^{-1}\text{m}^{-1}\). This follows by using the relation between current and charge, \(1\,\text{A}=1\,\text{C s}^{-1}\). What does this conversion mainly show?
ⓐ. It gives another derived unit for \(\vec{B}\)
ⓑ. It removes force from the unit of \(\vec{B}\)
ⓒ. It makes tesla and coulomb identical units
ⓓ. It changes current into a vector quantity
Correct Answer: It gives another derived unit for \(\vec{B}\)
Explanation: The relation \(1\,\text{A}=1\,\text{C s}^{-1}\) means that \(1\,\text{A}^{-1}=1\,\text{s C}^{-1}\). Substituting this into \(1\,\text{T}=1\,\text{N A}^{-1}\text{m}^{-1}\) gives \(1\,\text{T}=1\,\text{N s C}^{-1}\text{m}^{-1}\). This is only a different unit form of the same magnetic field unit. It does not make tesla identical to coulomb, because the full unit still contains \(\text{N}\), \(\text{s}\), \(\text{C}^{-1}\), and \(\text{m}^{-1}\). Unit conversions should preserve the physical quantity, not change it into a different quantity.
13. For the vector product \(\vec{v}\times\vec{B}\), the direction is
ⓐ. along \(\vec{v}\), in the plane of the two vectors
ⓑ. along \(\vec{B}\), in the plane of the two vectors
ⓒ. opposite to \(\vec{v}\) for every charge
ⓓ. perpendicular to both \(\vec{v}\) and \(\vec{B}\)
Correct Answer: perpendicular to both \(\vec{v}\) and \(\vec{B}\)
Explanation: A vector product produces a vector perpendicular to both vectors being multiplied. Therefore, \(\vec{v}\times\vec{B}\) is perpendicular to \(\vec{v}\) and also perpendicular to \(\vec{B}\). Its sense is decided by the right-hand rule, not by simply choosing the direction of either input vector. This idea is needed before using the magnetic force expression on a moving charge. The order also matters in a vector product, because \(\vec{B}\times\vec{v}\) would point in the opposite direction to \(\vec{v}\times\vec{B}\).
14. Use the arrangement described below: \(\vec{v}\) is along the positive \(x\)-axis and \(\vec{B}\) is along the positive \(y\)-axis. For a positive charge, the magnetic-force direction is along the direction of \(\vec{v}\times\vec{B}\). The direction of this force is
ⓐ. positive \(z\)-axis
ⓑ. negative \(z\)-axis
ⓒ. positive \(x\)-axis
ⓓ. positive \(y\)-axis
Correct Answer: positive \(z\)-axis
Explanation: The vector product direction is found by curling the fingers of the right hand from \(\vec{v}\) toward \(\vec{B}\). With \(\vec{v}\) along \(+x\) and \(\vec{B}\) along \(+y\), the thumb points along \(+z\). For a positive charge, the magnetic force has the same direction as \(\vec{v}\times\vec{B}\). The force is not along the velocity or along the magnetic field; it is perpendicular to both. This axis arrangement is the simplest way to see why magnetic-force direction is a three-dimensional idea.
15. Study the table and identify the only row in which both entries are properly matched.
| Row | Quantity | Nature or unit |
|---|
| P | \(\vec{B}\) | Scalar measured in \(\text{C}\) |
| Q | \(\vec{F}\) | Vector measured in \(\text{N}\) |
| R | \(I\) | Vector measured in \(\text{T}\) |
| S | \(\vec{A}\) | Scalar measured in \(\text{A m}^2\) |
ⓐ. Row P
ⓑ. Row Q
ⓒ. Row R
ⓓ. Row S
Correct Answer: Row Q
Explanation: Force \(\vec{F}\) is a vector quantity and its SI unit is newton, \(\text{N}\), so row Q is matched properly. Magnetic field \(\vec{B}\) is a vector and is measured in tesla, \(\text{T}\), not in coulomb. Current \(I\) is measured in ampere, \(\text{A}\), not in tesla, and it is not normally written with a vector arrow in elementary circuit notation. Area vector \(\vec{A}\) is a vector associated with surface orientation and has unit \(\text{m}^2\), while \(\text{A m}^2\) is the unit of magnetic moment. The row-wise comparison helps keep symbols, units, and vector notation separate.
16. A current loop has area vector \(\vec{A}\), current \(I\), and magnetic moment \(\vec{m}\). The relation \(m=NIA\) for an \(N\)-turn loop indicates that the unit of magnetic moment is
ⓐ. \(\text{T m}^{-2}\)
ⓑ. \(\text{A m}^2\)
ⓒ. \(\text{N C}^{-1}\)
ⓓ. \(\text{N s}^{-1}\)
Correct Answer: \(\text{A m}^2\)
Explanation: Magnetic moment magnitude for a current loop is \(m=NIA\). The number of turns \(N\) has no unit, current \(I\) has unit \(\text{A}\), and area \(A\) has unit \(\text{m}^2\). Multiplying these gives the unit \(\text{A m}^2\). This unit should not be confused with tesla, which is the unit of magnetic field \(\vec{B}\). The symbol \(m\) for magnetic moment also needs care because the same letter can represent mass in other formulas.
17. The area vector \(\vec{A}\) of a flat current loop is directed
ⓐ. along the tangent to the wire at every point
ⓑ. opposite to the current at all points
ⓒ. perpendicular to the plane of the loop
ⓓ. along the magnetic field only when field is absent
Correct Answer: perpendicular to the plane of the loop
Explanation: The area vector \(\vec{A}\) represents the orientation of a surface, so it is taken perpendicular to the plane of the loop. For a current loop, its direction is fixed by the right-hand thumb rule: curl the fingers in the direction of current and the thumb gives \(\vec{A}\). This direction later becomes important in defining magnetic moment \(\vec{m}=NI\vec{A}\). The vector \(\vec{A}\) should not be confused with the scalar area \(A\), which has only magnitude. A loop can have the same area but a different area-vector direction if the current direction is reversed.
18. A relation for the unit of magnetic field is written as \(1\,\text{T}=1\,\text{N s C}^{-1}\text{m}^{-1}\). The dimensional formula of \(\vec{B}\) is
ⓐ. \([M L T^{-2} A^{-1}]\)
ⓑ. \([M T^{-1} C^{-1}]\)
ⓒ. \([M T^{-2} A^{-1}]\)
ⓓ. \([M L^2 T^{-2} A^{-1}]\)
Correct Answer: \([M T^{-2} A^{-1}]\)
Explanation: \( \textbf{Unit relation:} \) The magnetic field unit may be written as \(1\,\text{T}=1\,\text{N A}^{-1}\text{m}^{-1}\).
\( \textbf{Dimensional form of force:} \)
\[
[\text{N}]=[M L T^{-2}]
\]
\( \textbf{Substitution in unit relation:} \)
\[
[\vec{B}]=[M L T^{-2}][A^{-1}][L^{-1}]
\]
\( \textbf{Cancel the length factor:} \)
\[
[\vec{B}]=[M T^{-2}A^{-1}]
\]
The length \(L\) cancels because the force relation uses force per unit current per unit length. Keeping an extra \(L\) in the answer would mean the conductor length was counted twice.
19. In a right-hand-rule orientation for \(\vec{v}\times\vec{B}\), the fingers are curled from \(\vec{v}\) toward \(\vec{B}\). The thumb gives
ⓐ. the direction of \(\vec{B}\) only
ⓑ. the direction of \(\vec{v}\) only
ⓒ. the direction opposite to \(\vec{v}\times\vec{B}\) for every charge
ⓓ. the direction of \(\vec{v}\times\vec{B}\)
Correct Answer: the direction of \(\vec{v}\times\vec{B}\)
Explanation: The right-hand rule gives the direction of the vector product \(\vec{v}\times\vec{B}\). The first vector \(\vec{v}\) is taken as the starting direction for the curl, and the second vector \(\vec{B}\) is the direction toward which the fingers curl. The thumb then points along the cross product. For a positive charge, magnetic force has the same direction as \(\vec{v}\times\vec{B}\), while for a negative charge it is reversed. The rule is about vector product direction first; charge sign is applied after finding \(\vec{v}\times\vec{B}\).
20. The quantity \(\vec{l}\) in the magnetic force relation for a straight current-carrying conductor represents
ⓐ. opposite conventional current, with magnitude \(l\)
ⓑ. along the magnetic field, with magnitude \(B\)
ⓒ. along conventional current, with magnitude \(l\)
ⓓ. normal to the conductor surface, with magnitude \(A\)
Correct Answer: along conventional current, with magnitude \(l\)
Explanation: In the relation \(\vec{F}=I\vec{l}\times\vec{B}\), \(\vec{l}\) is a vector along the conductor in the direction of conventional current. Its magnitude is the length \(l\) of the conductor segment considered. The vector nature matters because the force direction is decided by the cross product with \(\vec{B}\). A scalar length alone would not tell us the direction of force. This is why current direction must be stated before applying the magnetic-force rule to a wire.
