Mix Examples - Magnetic Effects of Electric Current Questions in English

(B) Electromagnetic induction is the phenomenon where an electromotive force $(EMF)$ or electric current is induced in a conductor when it is exposed to a changing magnetic field.
This principle was discovered by Michael Faraday.
It occurs when there is relative motion between a conductor and a magnetic field,or when the magnetic flux linked with a stationary conductor changes over time.

(N/A) Faraday's first law of electromagnetic induction states that whenever the magnetic flux linked with a closed circuit or coil changes,an induced electromotive force $(emf)$ is produced in the circuit.
This induced $emf$ persists only as long as the change in magnetic flux continues.

(N/A) Faraday's second law of electromagnetic induction states that the magnitude of the induced electromotive force $(emf)$ in a circuit is directly proportional to the rate of change of magnetic flux linked with the circuit.
Mathematically,it is expressed as $\varepsilon = -\frac{d\Phi_B}{dt}$,where $\varepsilon$ is the induced $emf$ and $\frac{d\Phi_B}{dt}$ is the rate of change of magnetic flux.

(B) Fleming's right-hand rule states that if you stretch the thumb,forefinger,and middle finger of your right hand such that they are mutually perpendicular to each other,then the thumb points in the direction of the motion of the conductor relative to the magnetic field,the forefinger points in the direction of the magnetic field,and the middle finger points in the direction of the induced current.

(N/A) According to Lenz's Law,the induced current will oppose the motion of the magnet. As the North pole $(N)$ of the magnet moves towards the coil,the coil will develop a North pole on its upper face to repel it. Therefore,the direction of the induced current,as seen from the top,will be anticlockwise.
$(b)$ As the North pole $(N)$ of the magnet moves towards the coil,the face of the coil facing the magnet will act as a North pole to oppose the motion. Looking from the right-hand side (where the magnet is approaching),the current will appear to flow in a clockwise direction.

(B) Alternating current $(AC)$ is defined as the current that changes its magnitude continuously and reverses its direction periodically over time.
In contrast,direct current $(DC)$ is the current that flows in a single constant direction and maintains a constant magnitude over time.
Therefore,the fundamental difference lies in the periodic reversal of direction and variation in magnitude characteristic of $AC$ compared to the steady nature of $DC$.

(N/A) In household electrical wiring,three types of wires are used based on their function:
$1$. Live wire: It is used to carry current from the source. According to the old convention,it is red in colour,and according to the new international convention,it is brown.
$2$. Neutral wire: It provides a return path for the current. According to the old convention,it is black in colour,and according to the new international convention,it is blue.
$3$. Earth wire: It is used for safety purposes to prevent electric shocks. It is green or yellow-green in colour.

(A) The two common types of wiring systems used for domestic purposes are the $Tree$ $system$ and the $Ring$ $system$.
In the $Tree$ $system$,the main supply is divided into several sub-circuits,which further branch out like a tree.
In the $Ring$ $system$,a ring circuit is formed where the supply cable starts from the distribution board,goes through all the points,and returns to the distribution board,allowing for multiple outlets to be connected to the same circuit.

(B) Earthing is a safety measure used to protect users from electric shocks.
If there is a fault in the appliance,such as a short circuit or insulation failure,the metal casing might become live.
Earthing provides a low-resistance path for the leakage current to flow directly into the ground,which triggers the circuit breaker or fuse to cut off the power supply.
This prevents the person operating the device from receiving a dangerous shock and protects the appliance from damage due to excessive current.

(C) In an electric circuit,the earthing or grounding wire is used to protect users from electric shocks.
According to the international colour code convention,the earthing wire is typically green or yellow in colour.

(B) To demonstrate the existence of a magnetic field around a current-carrying wire,we place a magnetic compass needle near the wire.
Since a magnetic compass needle is itself a small magnet,it experiences a force when placed in a magnetic field.
When the current flows through the wire,the needle shows a deflection,which confirms the presence of a magnetic field around the conductor.

(B) The strength $(B)$ of the magnetic field at a point near a current-carrying wire is directly proportional to the strength $(I)$ of the electric current flowing through the wire.
Mathematically,this is expressed as $B \propto I$.
This means that as the magnitude of the electric current increases,the strength of the magnetic field produced around the wire also increases.

(B) An alternating current $(AC)$ completes one full cycle by changing its direction twice.
Given that the frequency of the current is $50 \ Hz$, it means the current completes $50$ cycles in $1 \ second$.
Since the current changes its direction twice in every cycle, the total number of times it changes its direction in $1 \ second$ is $50 \times 2 = 100$ times.

(B) An alternating current $(AC)$ changes its direction twice in one complete cycle.
Given that the direction changes every $0.01\,s$,the time taken to complete one full cycle $(T)$ is $2 \times 0.01\,s = 0.02\,s$.
The frequency $(f)$ is the reciprocal of the time period $(T)$,given by $f = 1/T$.
Therefore,$f = 1 / 0.02 = 100 / 2 = 50\,Hz$.

(B) Short-circuiting in an electric circuit is a condition that occurs when the live wire comes into direct contact with the neutral wire.
This results in a very low resistance path for the current,causing a massive surge of current to flow through the circuit.
This sudden increase in current can lead to overheating,sparking,and potentially a fire.

(B) The space or region surrounding a magnet within which the force of attraction or repulsion can be detected by other magnetic materials is known as the magnetic field of the magnet.
In this region,the magnetic influence of the magnet is exerted on other magnets or magnetic substances.

(B) In case of a defect in any domestic appliance,current may leak to its metallic body.
The third wire of the earth connection provides a low-resistance path that transfers this leakage current directly to the earth.
As a result of this,the user of the appliance is protected from a potentially fatal electric shock.

(A) To demonstrate that the magnetic field decreases with distance,place a magnetic compass near a current-carrying wire.
Observe the deflection of the compass needle.
As you move the compass slowly away from the wire,the deflection of the needle decreases.
This reduction in deflection indicates that the strength of the magnetic field produced by the electric current decreases as the distance from the wire increases.

(A) $(i)$ Generator. An electric generator is a device that converts mechanical energy into electrical energy,thereby producing an electric current.
(ii) Voltmeter is used to measure the potential difference between two points in an electric circuit.
(iii) Ammeter is used to measure the magnitude of electric current in a circuit.
(iv) Galvanometer is used to detect the presence and direction of a small electric current in a circuit.

(B) Inside a solenoid,the magnetic field is uniform,which means the magnetic field lines are parallel to each other and run along the axis of the solenoid. Therefore,the shape of the magnetic field lines inside a solenoid is that of parallel straight lines.

(B) piece of magnetic material can be magnetised by placing it inside a current-carrying solenoid. The magnetic field produced by the solenoid aligns the magnetic domains within the material,thereby converting it into an electromagnet.

(D) According to Fleming's left-hand rule,the direction of the force on a moving charge is determined by the orientation of the magnetic field and the direction of the conventional current.
Since the electron is a negatively charged particle moving downwards,the direction of the conventional current is upwards.
The magnetic field is directed towards the right.
Applying Fleming's left-hand rule: point the index finger in the direction of the magnetic field (right),and the middle finger in the direction of the current (upwards). The thumb will point into the page.
Therefore,the force acting on the electron is directed into the page.

(N/A) The metallic body of electrical devices is connected to the earth wire to provide a low-resistance conducting path for any leakage current to flow directly to the earth. This process,known as earthing,ensures that the potential of the metallic body remains equal to that of the earth $(0 \ V)$. Consequently,if a fault occurs and the live wire touches the metallic casing,the current flows to the ground instead of through the user's body,thereby preventing severe electric shocks.

(N/A) circuit becomes overloaded when too many electrical appliances are connected to a single socket or circuit simultaneously. This causes the total current flowing through the circuit to exceed its rated capacity,leading to excessive heating of the wires and potential fire hazards.

(B) Short-circuiting occurs when the live wire and the neutral wire come into direct contact with each other.
This results in a very low resistance path,causing a massive amount of current to flow through the circuit.
This sudden surge of current can lead to sparks,overheating,and potentially electrical fires.

(B) In an $AC$ generator,the field magnet is used to produce a strong,uniform magnetic field. The armature coil of the generator rotates within this magnetic field,which induces an electromotive force $(EMF)$ or current in the coil according to Faraday's law of electromagnetic induction.

(A) Direct Current $(DC)$ flows in a constant direction and maintains a constant magnitude over time.
Since the current does not oscillate or change its direction periodically,it does not complete any cycles per second.
Therefore,the frequency of $DC$ is $0 \ Hz$.

(C) According to Faraday's law of electromagnetic induction, an induced current is generated only when there is a change in the magnetic flux $(\Phi_B)$ linked with the coil.
Magnetic flux is given by $\Phi_B = B \cdot A \cdot \cos(\theta)$, where $A$ is the area of the coil and $\theta$ is the angle between the magnetic field and the area vector.
Since the coil is moving with a uniform velocity $v$ in a uniform magnetic field $B$ and the area $A$ remains constant, the magnetic flux $\Phi_B$ linked with the coil does not change over time.
Since $\frac{d\Phi_B}{dt} = 0$, the induced electromotive force $(e = -\frac{d\Phi_B}{dt})$ is zero.
Therefore, the induced current in the coil is zero.

(C) According to Faraday's law of electromagnetic induction,the induced $emf$ is given by $\epsilon = -\frac{d\phi}{dt}$.
When the magnet is moved slowly,the rate of change of magnetic flux $\frac{d\phi}{dt}$ decreases,which causes the induced $emf$ to decrease.
The induced charge $q$ is given by $q = \int I dt = \int \frac{\epsilon}{R} dt = \int \frac{1}{R} \frac{d\phi}{dt} dt = \frac{\Delta\phi}{R}$.
Since the total change in magnetic flux $\Delta\phi$ and the resistance $R$ of the coil remain the same,the induced charge $q$ remains unchanged.

(B) The magnetic force $F$ on a charged particle moving in a magnetic field is given by the formula $F = qvB \sin(\theta)$,where $q$ is the charge,$v$ is the velocity,$B$ is the magnetic field strength,and $\theta$ is the angle between the velocity vector and the magnetic field vector.
Since the alpha particles are moving along (parallel to) the magnetic field,the angle $\theta = 0^\circ$.
Therefore,$\sin(0^\circ) = 0$.
Consequently,the magnetic force $F = qvB(0) = 0$.
Thus,the beam experiences zero magnetic force.

(A) current-carrying solenoid produces a magnetic field similar to that of a bar magnet.
One end of the solenoid acts as the North pole $(N)$,and the other end acts as the South pole $(S)$.
Therefore,it behaves exactly like a bar magnet.

(C) The force $F$ experienced by a current-carrying conductor of length $l$ carrying current $I$ in a magnetic field $B$ is given by the formula $F = BIl \sin(\theta)$,where $\theta$ is the angle between the direction of the current and the magnetic field.
Since the maximum value of $\sin(\theta)$ is $1$ (which occurs when $\theta = 90^{\circ}$),the force is largest when the current flows perpendicular to the applied magnetic field.

(D) The induced current in a secondary coil depends on the number of turns in the primary and secondary coils ($N_p$ and $N_s$) and the rate of change of magnetic flux.
According to the transformer principle,the ratio of currents is inversely proportional to the ratio of the number of turns: $\frac{I_s}{I_p} = \frac{N_p}{N_s}$.
If $N_s > N_p$ (step-up transformer),the secondary current $I_s$ will be less than the primary current $I_p$.
If $N_s < N_p$ (step-down transformer),the secondary current $I_s$ will be greater than the primary current $I_p$.
Therefore,the induced current in the secondary coil may be greater than or less than the current in the primary coil depending on the transformer design.

(N/A) Inside a solenoid,the magnetic field lines are in the form of parallel straight lines.
This pattern indicates that the magnetic field is uniform at all points inside the solenoid.

(B) The magnetic field produced inside a solenoid is strong and uniform.
When a soft iron rod is placed inside the solenoid,the magnetic field of the solenoid magnetises the soft iron.
This combination of a soft iron core and a current-carrying solenoid is known as an electromagnet.

(B) The right-hand thumb rule states that if you hold a current-carrying straight conductor in your right hand such that your thumb points in the direction of the current,then your fingers wrapped around the conductor will show the direction of the magnetic field lines.
Therefore,the thumb indicates the direction of the current.

(C) The force $F$ experienced by a current-carrying conductor of length $l$ carrying current $I$ placed in a magnetic field $B$ is given by the formula $F = BIl \sin(\theta)$,where $\theta$ is the angle between the direction of the current and the magnetic field.
Since the value of $\sin(\theta)$ is maximum $(1)$ when $\theta = 90^{\circ}$,the force experienced by the conductor is largest when the conductor is placed perpendicular to the magnetic field,i.e.,at an angle of $90^{\circ}$.

(N/A) Bring a magnetic needle near the wire.
$A$ current-carrying wire produces a magnetic field around it,which exerts a force on the magnetic needle,causing it to deflect.
$A$ wire without current does not produce a magnetic field,so the magnetic needle will remain stationary.

(C) Fleming's right-hand rule is used to determine the direction of the induced current in a conductor moving in a magnetic field.
According to this rule,if you stretch the thumb,forefinger,and middle finger of your right hand such that they are mutually perpendicular to each other,then:
$1$. The forefinger points in the direction of the magnetic field.
$2$. The thumb points in the direction of the motion of the conductor.
$3$. The middle finger points in the direction of the induced current.
Therefore,the thumb indicates the direction of motion of the conductor.

(N/A) By convention,magnetic field lines are considered to emerge from the $North$ $Pole$ and merge into the $South$ $Pole$ outside the magnet.
Inside the magnet,the direction of the field lines is from the $South$ $Pole$ to the $North$ $Pole$.
Since the field lines form a continuous path that starts and ends at the same point through the interior and exterior of the magnet,they are considered closed curves.

(N/A) An electric current can be induced in a coil by changing the magnetic field associated with it. One common method is to move a permanent magnet towards or away from the coil. As the magnet moves,the magnetic flux linked with the coil changes,which induces an electromotive force $(EMF)$ and consequently an electric current in the coil according to Faraday's Law of Electromagnetic Induction.

(N/A) The strength of an electromagnet can be increased by:
$(i)$ Increasing the number of turns of the wire in the solenoid.
$(ii)$ Increasing the magnitude of the electric current flowing through the solenoid.

(B) solenoid is defined as a long coil consisting of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder.
The primary difference lies in the magnetic field produced: inside a solenoid,the magnetic field is uniform and strong,resembling that of a bar magnet. In contrast,for a general coil,the magnetic field strength varies depending on the distance from the center and the geometry of the turns.

(N/A) According to Fleming's left-hand rule,if the forefinger points in the direction of the magnetic field and the central finger points in the direction of the current (the direction of motion of the positively charged alpha particle),then the thumb points in the direction of the force acting on the particle.
In this case,the magnetic field is directed upwards and the alpha particle is moving towards the right. Applying Fleming's left-hand rule,the force acting on the alpha particle will be directed out of the plane of the paper (perpendicular to the plane of the paper and towards the observer).

(100) The current changes its direction $100$ times in one second.
Reason: $A$ frequency of $50 \, Hz$ means that the alternating current completes $50$ cycles in one second.
In each cycle,the current changes its direction twice (once in the positive half-cycle and once in the negative half-cycle).
Therefore,the total number of direction changes in one second is $50 \times 2 = 100$ times.

(N/A) The type of electric current generated by most power stations in India is Alternating Current $(AC)$.
$(b)$ Alternating Current $(AC)$ is preferred over Direct Current $(DC)$ because it can be transmitted over long distances with minimal loss of electrical energy using step-up transformers.
$(c)$ The frequency of the power supply generated in India is $50 \ Hz$.

(N/A) $(i)$ $A$ current-carrying conductor produces a magnetic field around it. When a compass needle is brought near this conductor,the magnetic field of the conductor exerts a force on the magnetic needle,causing it to deflect.
$(ii)$ The strength of the magnetic field produced by a current-carrying conductor is directly proportional to the magnitude of the current flowing through it. Therefore,when the current in the conductor is increased,the magnetic field strength increases,which leads to a greater deflection of the compass needle.

(N/A) Outside the magnet,the magnetic field lines emerge from the north pole and merge into the south pole.
Inside the magnet,the direction of the field lines is from the south pole to the north pole.
Because the field lines are continuous and form a complete path from the north pole to the south pole outside and from the south pole to the north pole inside,they form closed curves.

(N/A) The relative strength of the magnetic field is indicated by the degree of closeness of the magnetic field lines. Where the field lines are crowded,the magnetic field is strong,and where they are far apart,the magnetic field is weak.
$(b)$ The strength of the magnetic field is highest near the poles of a bar magnet because the field lines are most concentrated there. Conversely,the strength of the magnetic field is lowest in the middle of the bar magnet,where the field lines are relatively far apart.

(N/A) The left figure represents the magnetic field lines produced by a current-carrying circular loop near its center,where the field lines appear as straight lines.
$(b)$ The right figure represents uniform magnetic field lines,which are produced by a long current-carrying solenoid.