RBSE Class 12 Physics Chapter 4 — Moving Charges and Magnetism: Most Repeated Questions (2013–2026)

Biot savart formula=| dB⃗ | =μ₀/4πIdlsinθ/r²

Let us take a circular loop of radius r carrying current I . We have to find the magnetic field at point P which is at axial distance a from the center. By resolving the magnetic field vector of every dl element, we can observe that all the cos component will cancel out whereas the sin component will add up:

So, B=∫dBsinα

B=∫μ₀Idlsinθsinα/(4π(√(r²+a²))²)

B=(μ₀Isin90^∘×sinα)/(4π(r²+a²))∫dl

> From the geometry, sinα=r/(√(r²+a²)) and ∫dl=2πr

B=μ₀I/(4π(r²+a²))(r/(√(r²+a²)))2πr; B=μ₀I2πr²/(4π(r²+a²)^3/2); B=μ₀Ir²/(2(r²+a²)^3/2); B=μ₀Ir²/(2(r²+a²)^3/2)

For N turns

B=μ₀NIr²/(2(r²+a²)^3/2)

If a=0

B=μ₀NIR²/(2(r²+a²)^3/2); B=μ₀NIR²/(2(r²)^3/2); B=μ₀NIR²/2r³; B=μ₀NI/2r

All solved questions for this chapter are in the full RBSE Physics PYQ book.

Ampère's Circuital Law states that the line integral of the magnetic field (B⃗) around any closed loop is equal to μ₀ times the net electric current ( I_enclosed ) passing through that loop

∮B⃗⋅dl⃗=μ₀I_enclosed

Let us take a solenoid carrying current I . If L is length of the solenoid, R is its radius, n is no. of turns and A is area of cross-section and it is kept in free space. Then also considering rectangular Ampère's loop of dimension l×b

Assuming, n=( no. of turns )/( length )⇒n=N/L

ACC. to A.C.L.:

⇒∮B⃗⋅dl⃗=μ₀I_enclosed ; ⇒∫_A^BB⃗⋅dl⃗+∫_B^CB⃗⋅dl⃗+∫_C^DB⃗⋅dl⃗+∫_D^AB⃗⋅dl⃗=μ₀I_enclosed ; ⇒∫_A^BBdlcos90^∘+∫_B^CBdlcos0^∘+∫_C^DBdlcos90^∘+0=μ₀I_enclos ; ⇒∫_B^CBdl=μ₀I_enclosed ; ⇒B∫_B^Cdl=μ₀I_enclosed ; ⇒B×l=μ₀(I× no. of turns ); ⇒Bl=μ₀(Inl) [ from (1)] ; ⇒B=μ₀nI= constant

All solved questions for this chapter are in the full RBSE Physics PYQ book.

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Magnetic field produced by (1) Wire on (2):

B₁=μ₀I₁/2πd; B₁=μ₀I₁/2πd

Force on (2) Wire due to B⃗ of (1) Wire:

F⃗₂=I₂l⃗×B⃗₁

F₂=I₂lB₁sinθ

F₂=I₂lB₁sin90^∘

F₂=I₂lμ₀I₁/2πd; F₂=μ₀I₁I₂l/2πd

Force per unit length (F/l) :

F₂/l=μ₀I₁I₂/2πd

F₁/l=μ₀I₁I₂/2πd

When current is parallel then forces are attractive and when current are antiparallel then forces are repulsive

Definition of 1 Ampere:

1 Ampere is the current which when passed through two parallel wires having distance of 1m between them, produces a force of 2×10^-7 N by 1m of their length

All solved questions for this chapter are in the full RBSE Physics PYQ book.

Construction:- A rectangular/circular coil of fine wire is wound on a light non-magnetic frame and suspended between the curved pole pieces of a strong permanent magnet, with a cylindrical soft iron core FIXED (stationary) at the centre to produce a radial field. It is the COIL — not the core — that is free to rotate; the coil is mounted on a spindle connected to the pointer at one end and a restoring spring at the other. Current through the coil produces a torque that rotates the coil (and pointer) until the spring's restoring torque balances it

Torque on coil = Torque on spring

BINA sinα=kθ

BINA sin90^∘=kθ

BINA =kθ (k= Spring cons. )

(BNA/k)I=θ

or, θ=GI (G= galvanometer constant )

So, θ∝I (G=BNA/k)

All solved questions for this chapter are in the full RBSE Physics PYQ book.