Bihar Board — Physics Numericals

Each chapter below contains 7 numerical problems. Answers are hidden — click Show Answer to reveal. Numbers and units follow SI unless mentioned otherwise.

Chapter: Electrostatics (7 numericals)

1. Two point charges +3 μC and -2 μC are separated by 5 cm. Calculate the magnitude of the electrostatic force between them. (k = 9×10⁹ N·m²/C²)
   21.6 N (attractive)
2. Two identical point charges +4 μC are 10 cm apart. Find the electric field at the midpoint.
   0 N/C (fields cancel)
3. A point charge of +6 μC is at the origin. Calculate the electric potential at a point 20 cm away. (k = 9×10⁹)
   V = kq/r = (9×10⁹)(6×10^-6)/0.2 = 270000 V = 2.7×10⁵ V
4. A particle of charge -2 μC is moved from point A at 0.1 m from a +5 μC charge to point B at 0.2 m. Find the work done by the electric force (k = 9×10⁹).
   (Take work = change in electric potential energy.)
   W = k·Q·q(1/r_B − 1/r_A) = (9×10⁹)(5×10^-6)(−2×10^-6)(1/0.2 − 1/0.1) = −0.054 J
5. A small sphere initially has charge +8 μC. It is then split into two identical pieces carrying +5 μC and +3 μC. Verify charge conservation (total charge).
   Total charge = +5 μC + +3 μC = +8 μC (conserved)
6. Three charges +2 μC, +2 μC and −4 μC are placed at the vertices of an equilateral triangle (side = 0.1 m). What is the net charge of the system?
   Net charge = 2 + 2 − 4 = 0 μC
7. If a 1 μC test charge experiences an electrostatic force of 0.02 N, what is the electric field at that location?
   E = F/q = 0.02 N / 1×10^-6 C = 2.0×10⁴ N/C

Chapter: Electric Potential & Capacitance (7 numericals)

1. Find the capacitance of a parallel-plate capacitor with plate area 0.02 m² and separation 1 mm. (ε₀=8.85×10^-12 F/m)
   C = ε0 A / d = (8.85×10^-12)(0.02)/(1×10^-3) = 1.77×10^-10 F = 177 pF
2. A 10 μF capacitor is charged to 12 V. Calculate the charge stored.
   Q = CV = 10×10^-6 × 12 = 1.2×10^-4 C = 120 μC
3. Two capacitors of 5 μF and 10 μF are connected in series across 12 V. Find the equivalent capacitance.
   1/C_eq = 1/5 + 1/10 → C_eq = 1/(0.2+0.1) μF = 1/0.3 μF = 3.333... μF → 3.33 μF
4. Energy stored in a 2 μF capacitor charged to 100 V. Compute.
U = 1/2 CV² = 0.5 × 2×10^-6 × (100)² = 0.01 J
5. A 4 μF and 6 μF capacitors are connected in parallel across 20 V. Find the total charge stored.
   C_total = 10 μF → Q_total = C_total × V = 10×10^-6 × 20 = 2.0×10^-4 C = 200 μC
6. A capacitor of capacitance 8 μF stores energy 0.02 J. Find the voltage across it.
   U = 1/2 CV² → V = √(2U/C) = √(2×0.02 / 8×10^-6) = √(5000) ≈ 70.71 V
7. If the distance between plates of a parallel-plate capacitor is doubled (charge kept fixed), how does the capacitance change?
   Capacitance halves (C ∝ 1/d). No numerical value — qualitative answer required.

Chapter: Moving Charges & Magnetism (7 numericals)

1. A charge of 2 μC moves with speed 1×10⁵ m/s perpendicular to a magnetic field of 0.2 T. Find the magnetic force on it.
   F = qvB = 2×10^-6 × 1×10⁵ × 0.2 = 0.04 N
2. An electron (charge 1.6×10^-19 C) moves at 2×10⁶ m/s in a magnetic field of 0.1 T perpendicular to v. Find the force.
   F = qvB = 1.6×10^-19 × 2×10⁶ × 0.1 = 3.2×10^-14 N
3. A proton (m = 1.67×10^-27 kg, q = 1.6×10^-19 C) enters a magnetic field of 0.05 T with speed 1×10⁶ m/s perpendicular to the field. Calculate the radius of its circular path.
   r = mv/(qB) = (1.67×10^-27 × 1×10⁶)/(1.6×10^-19 × 0.05) ≈ 0.2087 m ≈ 0.209 m
4. Current 0.5 A flows in a straight wire of length 0.2 m placed perpendicular to a magnetic field of 0.3 T. Find the magnetic force on the wire.
   F = I L B = 0.5 × 0.2 × 0.3 = 0.03 N
5. What is the magnetic force on a charged particle moving exactly parallel to the magnetic field? (qualitative)
   Force = 0 (because v is parallel to B, F = qvB sinθ with θ = 0)
6. Magnetic field at the centre of a circular loop of radius 0.05 m carrying current 2 A. (μ₀=4π×10^-7 T·m/A)
   B = μ0 I /(2R) = (4π×10^-7 × 2)/(2×0.05) = 2.51×10^-5 T ≈ 2.51×10^-5 T
7. Torque on a rectangular loop of sides 0.1 m and 0.05 m carrying current 3 A in a magnetic field 0.4 T, when plane of loop is perpendicular to B (maximum torque).
   Area = 0.1×0.05 = 0.005 m². τ = N I A B = 1×3×0.005×0.4 = 0.006 N·m

Chapter: Magnetism & Matter (7 numericals)

1. Given magnetisation M = 200 A/m when H = 100 A/m. Find magnetic susceptibility χ.
χ = M/H = 200/100 = 2.0
2. A rod is placed in field H = 500 A/m. If susceptibility χ = 0.002, find magnetisation M.
   M = χ H = 0.002 × 500 = 1.0 A/m
3. If the susceptibility of a material is χ = −1×10⁻⁵, what type of magnetic behaviour does it show?
   Diamagnetic (negative, very small susceptibility)
4. Find the relative permeability μ_r for χ = 0.002.
   μr = 1 + χ = 1 + 0.002 = 1.002
5. Magnetic moment of a current loop with I = 2 A and area A = 0.01 m².
   μ = I A = 2 × 0.01 = 0.02 A·m²
6. If magnetisation M = 400 A/m for a sample of volume 0.001 m³, find magnetic moment.
   Magnetic moment = M × V = 400 × 0.001 = 0.4 A·m²
7. For a sample with χ = 0.01 and H = 200 A/m, compute magnetic flux density B (use μ0 = 4π×10^-7 T·m/A and M = χH).
   M = χH = 0.01×200 = 2 A/m. B = μ0 (H + M) = 4π×10^-7 × (200 + 2) ≈ 2.53×10^-4 T

Chapter: Current Electricity (7 numericals)

1. A resistor of 10 Ω is connected across 12 V. Find the current through it.
   I = V/R = 12/10 = 1.2 A
2. Find equivalent resistance of three resistors 2 Ω, 3 Ω, 6 Ω connected in series.
   R = 2 + 3 + 6 = 11 Ω
3. Find equivalent resistance of the same resistors (2 Ω, 3 Ω, 6 Ω) connected in parallel.
   1/R = 1/2 + 1/3 + 1/6 = 1 → R = 1 Ω
4. A wire of length 2 m and cross-sectional area 1×10^-6 m² has resistivity 1.7×10^-8 Ω·m. Find its resistance.
   R = ρ L / A = (1.7×10^-8 × 2) / 1×10^-6 = 3.4×10^-2 Ω = 0.034 Ω
5. Power dissipated in a 5 Ω resistor carrying 2 A current.
   P = I²R = 2² × 5 = 20 W
6. A cell of emf 12 V and internal resistance 1 Ω is connected to a load of 5 Ω. Find the current delivered by the cell.
   I = emf/(R + r) = 12/(5 + 1) = 2 A
7. How much charge passes through a conductor when a current of 2 A flows for 3 minutes?
   Q = I t = 2 × (3×60) = 360 C

Prepared for Bihar Board style practice — numericals avoid lengthy algebra and use SI units. If you want: (a) printable PDF, (b) Hindi version, or (c) solution steps instead of only final answers, tell me and I will update.