Solved Examples
A dedicated bank of worked problems. Key rules to recall:
- Right-hand thumb rule - field around a straight conductor (thumb = current, fingers = field).
- Fleming's left-hand rule - force on a current in a field (Fore = Field, ceNtre = curreNt, thuMb = Motion). Motor.
- Fleming's right-hand rule - induced current in a generator (thumb = motion, fore = field, middle = induced current).
- Household supply: AC, 220 V, 50 Hz; Live = red, Neutral = black, Earth = green.
Example 1: Field of a power line (NCERT 12.1) Current flows east to west in a horizontal power line. Field below and above it? Solution: By the right-hand thumb rule the circular field is clockwise viewed from the east; below the wire it points north, above it points south.
Example 2: Force on an electron (NCERT 12.2) An electron enters a field (into the page) moving right. Direction of the force? Solution: Conventional current is opposite the electron (i.e. to the left). By Fleming's left-hand rule the force is into the page (option d in NCERT).
Example 3: Alpha particle deflection (NCERT Q) A positively charged alpha particle moving west is deflected north by a field. Direction of the field? Solution: Current = west (positive charge motion), force = north. By Fleming's left-hand rule the field points upward (option d).
Example 4: Properties of field lines (NCERT Q) List the properties of magnetic field lines. Solution: (i) They emerge from N and merge at S outside the magnet, forming closed loops. (ii) The tangent gives the field direction. (iii) They are crowded where the field is strong. (iv) No two field lines cross.
Example 5: Why field lines do not cross (NCERT Q) Why don't two magnetic field lines intersect each other? Solution: If they crossed, at the intersection a compass needle would have to point in two directions at once, which is impossible. Hence field lines never cross.
Example 6: Field inside a solenoid (NCERT MCQ) The magnetic field inside a long straight current-carrying solenoid is _. Solution: It is the same at all points (uniform) - the field lines inside are parallel and equally spaced.
Example 7: Field of a clockwise loop (NCERT Q) A circular loop lies on the table with current flowing clockwise (viewed from above). Field inside and outside? Solution: By the right-hand rule, the field inside the loop points downward (into the table) and the return field outside points upward.
Example 8: Which proton property changes (NCERT Q) Which property of a proton can change while it moves freely in a magnetic field? Solution: The magnetic force changes the proton's velocity, momentum (direction) but not its mass and not its speed (the magnetic force does no work). So velocity and momentum can change.
Example 9: Displacement of rod AB (NCERT Q) How is the displacement of a current-carrying rod in a field affected by (i) more current, (ii) a stronger magnet, (iii) a longer rod? Solution: The force - and hence displacement - increases in all three cases: larger current, stronger field, and longer conductor each increase the force.
Example 10: Two methods of producing magnetic fields (NCERT Q) List two methods of producing magnetic fields. Solution: (i) Using a permanent magnet (bar magnet). (ii) Passing an electric current through a conductor (straight wire, coil, or solenoid) - a current-carrying conductor produces a magnetic field.
Example 11: When is the force largest? (NCERT Q) When is the force on a current-carrying conductor in a magnetic field the largest? Solution: When the direction of the current is at right angles (perpendicular) to the direction of the magnetic field.
Example 12: Electron beam deflection (NCERT Q) An electron beam moving horizontally (back to front) is deflected to your right by a magnetic field. Direction of the field? Solution: Conventional current is front to back (opposite the electrons). Force is to the right. By Fleming's left-hand rule the field points vertically downward.
Example 13: Three direction rules (NCERT Q) State the rule for the direction of (i) field around a straight conductor, (ii) force on a conductor, (iii) current induced in a rotating coil. Solution: (i) Right-hand thumb rule, (ii) Fleming's left-hand rule, (iii) Fleming's right-hand rule.
Example 14: Oven on a 5 A circuit (NCERT Q) A 2 kW oven runs on a 220 V circuit rated 5 A. What happens? Solution: A > 5 A. The fuse blows and breaks the circuit; the oven cannot run on this circuit.
Example 15: Function of the earth wire (NCERT Q) What is the function of an earth wire and why earth metallic appliances? Solution: The earth wire provides a low-resistance path to the ground. Earthing keeps the appliance's metal body at earth potential, so any leakage current goes to earth and the user does not get a severe shock.
Example 16: When does a short circuit occur? (NCERT Q) When does an electric short circuit occur? Solution: When the live and neutral wires come into direct contact (damaged insulation or a fault), the resistance falls and the current rises abruptly - a short circuit.
Example 17: Field near a long straight wire (NCERT MCQ) Which describes the field near a long straight current-carrying wire? Solution: Concentric circles centred on the wire (option d). Not radial, not parallel to the wire.
Example 18: True/false on field lines (NCERT Q) (a) The field at the centre of a long circular coil is parallel straight lines. (b) A green-insulation wire is the live wire. Solution: (a) True - at the centre the field lines are nearly parallel straight lines. (b) False - a green wire is the earth wire; the live wire is red.
Example 19: Motor vs generator State the energy conversion and the hand-rule for a motor and a generator. Solution: Motor: electrical → mechanical, Fleming's left-hand rule. Generator: mechanical → electrical, Fleming's right-hand rule.
Example 20: Role of split-ring commutator Why is a split-ring commutator used in a DC motor? Solution: It reverses the current in the coil every half rotation, so the torque always acts in the same rotational sense and the coil rotates continuously in one direction.
Example 21: AC vs DC generator ring What distinguishes an AC generator from a DC generator? Solution: An AC generator uses two slip rings (output reverses each half turn = AC); a DC generator uses a split-ring commutator (output stays one-directional = DC).
Example 22: Current drawn by an appliance A 1000 W heater runs on 220 V mains. What current does it draw, and which fuse (5 A or 15 A) circuit should it be on? Solution: A. It is below 5 A, so it can safely run on the 5 A circuit (a 5 A fuse is suitable).
Example 23: Uniform field diagram (NCERT Q) How do you represent a uniform magnetic field in a diagram? Solution: By parallel, equally spaced straight field lines all pointing in the same direction (as inside a long solenoid).
Example 24: Precaution against overloading (NCERT Q) What precaution avoids overloading of domestic circuits? Solution: Do not connect too many appliances (especially high-power ones) to a single socket, use separate properly rated circuits (5 A, 15 A), and use a fuse of correct rating.
Example 25: Frequency of AC The AC mains reverses direction 50 times per second. What is its frequency, and what is the supply voltage in Indian homes? Solution: Frequency = 50 Hz; supply voltage = 220 V (AC).
Example 26: Field of a coil with n turns A single circular turn produces a field B at its centre. What field does a coil of 20 such turns produce? Solution: Each turn adds up, so the field is 20 B (n times that of one turn), since all turns carry current in the same direction.
Example 27: Direction of field, current up A wire carries current vertically upward. Using the right-hand thumb rule, describe the field lines. Solution: With the thumb pointing up (current), the fingers curl anticlockwise (viewed from above) - the concentric field circles run anticlockwise around the wire.
Example 28: Soft iron vs steel core Why is soft iron preferred over steel for the core of an electromagnet? Solution: Soft iron is a temporary magnet - it magnetises strongly with current and loses magnetism when the current stops, so the electromagnet can be turned on and off. Steel retains magnetism (permanent), which is unwanted.
Example 29: Why household wiring is parallel Give two reasons appliances at home are wired in parallel across the mains. Solution: (i) Each appliance gets the full 220 V. (ii) Each has its own switch and if one appliance fails or is off, the others keep working. Parallel wiring also lets each draw the current it needs.
Example 30: MRI and body magnetism (More to Know) On what principle does MRI rely, and which body organs produce significant magnetic fields? Solution: MRI (Magnetic Resonance Imaging) uses the magnetic fields produced inside the body by weak ion currents to image body parts. The heart and the brain produce the most significant magnetic fields.
Example 31: Direction of force reversed List two ways to reverse the direction of the force on a current-carrying conductor in a magnetic field. Solution: (i) Reverse the direction of the current, or (ii) reverse the direction of the magnetic field (interchange the magnet's poles). Either one reverses the force.
Example 32: Identify the device A device has a coil rotating in a magnetic field with two slip rings and brushes, and it lights a bulb when the coil is turned by hand. Name it and its energy conversion. Solution: It is an AC generator (dynamo). It converts mechanical energy into electrical energy by electromagnetic induction.