“Moving Charges and Magnetism NCERT Book Back Exercise Solutions | Complete CBSE Board, NEET & JEE Main Study Guide 2026-27”

Chapter 4 — Moving Charges and Magnetism

Complete NCERT Solution Manual (CBSE Board Examiner Style)

Prepared for: CBSE Class 12 Physics | Board Exam, NEET, and JEE Main Preparation Based on: NCERT Textbook, Latest CBSE Marking Scheme and Syllabus (2025–26) Style: Full-marks board-examiner answer writing

Question 4.1

Question: A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

Marks Weightage: 2 Marks

Concepts Tested: – Magnetic field due to a circular current loop – Superposition of field due to N turns

Solution:

Common Errors: Forgetting unit conversion (cm→m); using diameter instead of radius; omitting N (number of turns).

NEET Connection: NEET frequently asks a direct one-step numerical exactly like this, often testing whether students confuse  with diameter.

JEE Main Connection: JEE often extends this into a multi-turn coil combined with a straight wire segment, requiring superposition of the two field contributions at a common point.

Real-Life Application: This is the operating principle of the field coil in moving-coil galvanometers, small electromagnets, and Helmholtz coil pairs used in laboratories to produce known uniform fields.

Previous Year CBSE Connection: Direct variants of this numerical (with different N, R, I) have appeared in CBSE board papers and pre-boards multiple times as a straightforward 2-mark numerical, generally rated Easy.

Question 4.2

Question: A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?

Marks Weightage: 2 Marks

Concepts Tested: Magnetic field due to an infinite straight current-carrying conductor; Ampere’s Circuital Law application.

Common Errors: Using the coil formula by mistake; forgetting to double the radius or halve incorrectly.

NEET Connection: A staple NEET one-liner, sometimes combined with direction (right-hand thumb rule) as an assertion-reason question.

JEE Main Connection: JEE extends this to superposition of fields from two parallel wires or to a point equidistant from multiple wires, requiring vector addition.

Real-Life Application: Basis of current-carrying overhead cables’ stray magnetic fields, used in current-sensing Hall probes and clamp meters.

Previous Year CBSE Connection: A near-identical numerical (different I, r) has appeared in CBSE board papers as a 2-mark question; Easy difficulty

Question 4.3

Question: A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.

Marks Weightage: 2 Marks

Concepts Tested: Field due to straight wire; Maxwell’s right-hand thumb rule for direction.

Common Errors: Reversing the current direction; confusing “up” and “down” because of unfamiliarity visualising 3-D compass geometry on paper.

NEET Connection: This exact question is a frequently recycled NEET MCQ with distractors testing sign/direction errors.

JEE Main Connection: JEE often asks for the net field from two such wires in perpendicular directions, requiring vector addition of magnitude and direction.

Real-Life Application: Compass deflection near underground/overhead power lines is explained by exactly this calculation.

Previous Year CBSE Connection: Appears almost verbatim in several CBSE sample papers; Easy–Medium (medium only because of the direction component).

Question 4.4

Question: A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?

Marks Weightage: 2 Marks

Concepts Tested: Field due to straight wire; direction via right-hand rule below the wire.

Common Errors: Mixing up “below” with “east of,” leading to a wrong direction (north/south instead of up/down or vice-versa).

NEET Connection: Frequently tested with power-line safety context (why compasses near power lines deviate).

JEE Main Connection: JEE variants ask for the net field at a point below the wire combined with Earth’s horizontal field, requiring vector resultant magnitude and angle.

Real-Life Application: Overhead transmission line safety clearances and electromagnetic interference calculations for structures beneath power lines.

Previous Year CBSE Connection: A standard 2-mark CBSE numerical, appearing in various board years with different current/distance values; Easy.

Question 4.5

Question: What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30° with the direction of a uniform magnetic field of 0.15 T?

Marks Weightage: 2 Marks

Concepts Tested: Force on a current-carrying conductor in a magnetic field.

Common Errors: Omitting ; using  instead of  (confusing with torque’s  dependence in some formulations).

NEET Connection: A very common one-step NEET numerical, sometimes disguised with the angle given between wire and field lines vs wire and normal — read carefully.

JEE Main Connection: JEE extends this to variable-angle wires (e.g. a semicircular or bent wire) requiring integration or vector decomposition.

Real-Life Application: Basis of the force experienced by wires in a loudspeaker voice coil and in electric motor windings.

Previous Year CBSE Connection: Frequently appears as a direct 2-mark numerical in CBSE papers; Easy.

Question 4.6

Question: A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?

Marks Weightage: 2 Marks

Concepts Tested: Force on current-carrying wire in a uniform field (solenoid interior); Fleming’s left-hand rule for direction.

Common Errors: Forgetting cm→m conversion; using  despite the perpendicular condition stated.

NEET Connection: Common NEET numerical combined with solenoid field formula in a two-step problem.

JEE Main Connection: JEE often combines this with computing  from solenoid parameters first (two-step numerical), as seen in Q4.8 below.

Real-Life Application: The working principle of relays and solenoid valves, where a wire/armature inside a solenoid experiences force to actuate a mechanical switch.

Previous Year CBSE Connection: Direct 2-mark CBSE numerical, appears in multiple year papers; Easy.

Question 4.7

Question: Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

Marks Weightage: 3 Marks

Concepts Tested: Force between two parallel current-carrying conductors; attraction/repulsion rule.

Common Errors: Forgetting to convert both cm values; reporting force per unit length instead of total force (or vice-versa) when the question asks for one specific quantity.

NEET Connection: This is the numerical basis of the SI (now redefined) definition of the ampere, frequently referenced in NEET conceptual MCQs.

JEE Main Connection: JEE often asks for the net force on a wire due to two other parallel wires on either side, requiring vector addition of attractive/repulsive contributions.

Real-Life Application: Explains busbar spacing design in power distribution systems (large currents can produce significant mechanical forces on closely spaced conductors, e.g., during short-circuit fault currents).

Previous Year CBSE Connection: Frequently asked as a 3-mark CBSE numerical with an added “attractive or repulsive, why?” sub-part; Medium difficulty because of the two-step calculation.

Question 4.8

Question: A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.

Marks Weightage: 3 Marks

Concepts Tested: Magnetic field inside a long solenoid; turns density calculation.

Common Errors: Using total turns  directly in place of ; using diameter as if it were relevant to the field magnitude; forgetting to convert length to metres.

NEET Connection: A staple NEET numerical; distractors often test whether students correctly compute  from layered windings.

JEE Main Connection: JEE frequently follows this with a second part asking for force on a current-carrying wire placed inside (as in Q4.6), making it a compound two-concept problem.

Real-Life Application: Design basis for solenoid electromagnets, MRI magnet coils (superconducting solenoids), and inductors in circuits.

Previous Year CBSE Connection: A very frequently repeated 3-mark CBSE numerical across multiple years; Medium (multi-step).

Question 4.9

Question: A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30° with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?

Marks Weightage: 2 Marks

Concepts Tested: Torque on a current-carrying coil in a magnetic field.

Common Errors: Using  instead of  (angle-between-plane-and-B confusion); forgetting .

NEET Connection: Very frequently tested; NEET often varies whether the angle given is with the plane or the normal.

JEE Main Connection: JEE extends this into the full oscillation/restoring-torque problem for a coil (leading into moving-coil galvanometer derivations).

Real-Life Application: The fundamental torque equation behind every electric motor and moving-coil galvanometer/ammeter design.

Previous Year CBSE Connection: A very frequently repeated 2–3 mark CBSE numerical; Easy–Medium.

Question 4.10

Question: Two moving coil meters, M₁ and M₂, have the following particulars: , , , ; , , , . (The spring constants are identical for the two meters.) Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M₂ and M₁.

Marks Weightage: 3 Marks

Concepts Tested: Current sensitivity and voltage sensitivity of a moving-coil galvanometer.

Common Errors: Forgetting to divide by  for voltage sensitivity; mixing up which meter is numerator vs denominator (question asks ratio of M₂ to M₁).

NEET Connection: A conceptual favourite — NEET often asks which sensitivity increases when a shunt or series resistance is added.

JEE Main Connection: JEE extends this into design questions: “how should N, B, A, k be changed to double the current sensitivity without changing voltage sensitivity,” requiring simultaneous adjustment of .

Real-Life Application: Central to the design trade-offs in analogue ammeters and voltmeters converted from a base galvanometer.

Previous Year CBSE Connection: This exact comparative-ratio numerical is a CBSE board favourite, appearing in several years; Medium difficulty.

Question 4.11

Question: In a chamber, a uniform magnetic field of 6.5 G (1 G = 10⁻⁴ T) is maintained. An electron is shot into the field with a speed of 4.8×10⁶ m/s normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. ( , )

Marks Weightage: 3 Marks

Concepts Tested: Circular motion of a charged particle in a magnetic field; centripetal force = magnetic force.

Common Errors: Forgetting to convert gauss to tesla; treating the electron’s charge as positive without noting it does not affect radius magnitude (though it does affect direction of curving).

NEET Connection: One of the most repeated NEET numericals in the whole syllabus — memorise this method thoroughly.

JEE Main Connection: JEE typically extends this into finding the time period or combining with an electric field (velocity selector, Q4.20-type problems).

Real-Life Application: Underlies the design of mass spectrometers, cyclotrons, and cathode-ray tube electron-beam steering (historical CRT televisions/oscilloscopes).

Previous Year CBSE Connection: A perennial CBSE board favourite (3 marks), appearing almost every year in some form; Medium.

Question 4.12

Question: In Exercise 4.11, obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

Marks Weightage: 2 Marks

Concepts Tested: Cyclotron frequency; independence of frequency from speed.

Common Errors: Re-deriving from scratch using  and then forgetting to show the cancellation; numerical slips in the  factor.

NEET Connection: A classic NEET conceptual MCQ: “cyclotron frequency depends on…” with speed/radius as tempting wrong options.

JEE Main Connection: This principle is foundational to JEE’s cyclotron numerical (see Q4.25) — always connect this concept when solving cyclotron problems.

Real-Life Application: The entire cyclotron particle accelerator design relies on this speed-independent frequency (until relativistic effects become significant at very high speeds).

Previous Year CBSE Connection: Frequently paired with Q4.11 as a two-part 2+3 mark CBSE question; Medium (due to the explanation requirement).

Question 4.13

Question: (a) A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an angle of 60° with the normal of the coil. Calculate the magnitude of the counter-torque that must be applied to prevent the coil from turning. (b) Would your answer change if the circular coil were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars unaltered.)

Marks Weightage: 3 Marks

Concepts Tested: Torque on a current loop; independence of torque from loop shape (dependence only on enclosed area).

Common Errors: Recomputing area incorrectly for the “irregular” shape rather than recognising it is stated to be equal.

NEET Connection: A common conceptual NEET MCQ testing shape-independence of magnetic moment/torque.

JEE Main Connection: JEE extends this into magnetic-moment calculations for compound/composite loop shapes using the area-vector addition principle.

Real-Life Application: Explains why irregularly wound motor/generator coils still function predictably as long as enclosed area and turns are controlled.

Previous Year CBSE Connection: Appears periodically as a “reasoning + numerical” combination question; Medium.