Chapter 4 Moving Charges and Magnetism
- When current is passed through the conductor, the compass needle deflects. Why? The compass needle is now subjected to the earth’s magnetic field and the magnetic field of the straight conductor. 1
- The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). I = 300 A, l = 70 cm, r = 1.5 cm F = fracμ₀ I₁ I₂2 π r = frac4 π × 10⁻⁵ × 300 × 3002 × 1.5 × 10⁻² = 1.2 N The force is repulsive. 1
- An electron travelling west to east enters a chamber having a uniform electrostatic field The force on the electron due to the electric field is south to north. To oppose this the force due to the magnetic field should be to the s... 1
- A charged particle enters an environment of a strong and non-uniform magnetic field varying from point A space-fixed magnetic field cannot do work on moving charge and hence the speed remains the same (so also KE). 1
- A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) The force on a charged particle moving in a magnetic field is F = q( v x B ) = qvB sin θ. If θ = 0° or 180°, force is zero and the particle... 1
- In Exercise. 11 obtain the frequency of revolution of the electron in its circular orbit Frequency in Exercise 11, υ = qB / 2πm = frac1.6 × 10⁻¹⁹ × 6.5 × 10⁻⁴2 × π × 9.1 × 10⁻³¹ = 18 MHz 2
- In a chamber, a uniform magnetic field of 6.5G (1G = 10-4 T) is maintained. B = 6.5 x 10⁻⁴ T, v = 4.8 x 10⁶ms⁻¹ Bqv = fracmv²r r = mv / qB = frac9.1 × 10⁻³¹ × 4.8 × 10⁶1.6 × 10⁻¹⁹ × 6.5 × 10⁻⁴ = 4.2 x 10⁻²m = 4.2 cm 2
- A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended I = 12A n = 20 B = 0.80 T θ =30° A = 10 x 10= 100cm² = 100 x 10⁴m² τ = n BIA sin θ = 2d x 0.80 x l00 x l0^(-4 )x l2 x sin30° = 0.96 Nm. 1
- 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. l = 80 cm = 80 x 10⁻² m p = 5 N = 400 n = N / l = frac40080 × 10⁻² = 500 For one turn, B = μ₀nl B = 4π x 10⁻⁷ x 500 x 8 For p turns = pB = 5... 1
- Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A I₁ = 8.0 A I₂ = 5.0 A r = 4.0 cm = 4.0 x 10^(-2 )m l = 10 cm = 0.1 m F = frac2 × 10⁻⁷ I₁ I₂ lr = frac2 × 10⁻⁷ × 8 × 5 × 0.14 × 10⁻² = 2 x 10... 1
- A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis I = 3.0 cm = 3.0 x 10⁻² m I = 10 A B = 0.27 T F = BIl = 0.27 x 10 x 3 x 10⁻² = 8.1 x 10⁻² N 1
- What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle I = 8A, B = 0.15 T and θ = 30° F = BI1 sin θ Therefore, force per unit length on the wire, F = 0.15 × 8 x 1 x sin30° = 0.15 x 8 x 1 x 0.5 =... 1
- A horizontal overhead power line carries a current of 90 A in east to west direction. I = 90 A, r = 1.5 m B = fracμ₀ I2 π r = frac4 π × 10⁻⁷ × 902 π × 1.5 = 1.2 x 10⁻⁵ T (South) 1
- A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude I = 50 A, r = 2.5 m B = fracμ₀ I2 π r = frac4 π × 10⁻⁷ × 502 π × 2.5 = 4 x 10⁻⁶ T upwards. (due to the wire alone) 1
- 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 w ire? I = 35 A, r = 20 cm = 20 x 10⁻² m B = fracμ₀ I2 π r = frac4 π × 10⁻⁷ × 352 π × 20 × 10⁻² = 3.5 x 10^(-5 )T 1
- A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. n = 100, I = 0.40 A, r = 8.0 cm = 8.0 x 10⁻² m B = fracμ₀ nI2 r = frac4 π × 10⁻⁷ × 100 × 0.42 × 8 × 10⁻² = π x 10^(-4 )T 1