Moving Charges and Magnetism

Moving Charges and MagnetismNEET Physics · Class 12 · NCERT Chapter 4

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7 interactive concept widgets for Moving Charges and Magnetism. Drag any slider, change any number, and watch the formula and the answer update live. Built so you understand how each NEET problem actually works, not just the final number.

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Lorentz force calculator

Charged particle in B field

Field of a straight wire

Field of a circular coil

Field of a solenoid

Force between parallel wires

Torque on a current loop

Force and motion

Lorentz force on a moving charge, plus the resulting circular motion in a uniform field.

Lorentz force

Lorentz force calculator

Force on a charged particle moving in a magnetic field.

Magnetic force on a moving charge: F = q v B sin theta. Maximum when v is perpendicular to B; zero when parallel.

q: 1.60e-19 C

v: 1.00e+6 m/s

B: 0.50 T

θ between v and B: 90°

Magnetic force F

8.000e-14 N

F = q v B sin θ

Try this

θ = 0° (v parallel to B): no force.
θ = 90°: maximum force, F = qvB.
For an electron (q = -e), force is opposite to qv × B.
Magnetic force never does work: it always points perpendicular to v.

Circular motion

Charged particle in a magnetic field

Radius and period for a particle moving perpendicular to B.

With v perpendicular to B, the magnetic force becomes the centripetal force, so the particle moves in a circle. Radius depends on speed; period does not.

m: 9.11e-31 kg

v: 1.00e+6 m/s

q: 1.60e-19 C

B: 0.50 T

Radius

1.139e-5 m

r = \frac{m v}{q B}

Time period T

7.15e-11 s

Frequency f

1.40e+10 Hz

T = \frac{2 π m}{q B}

Try this

Period T does NOT depend on v. Faster particles trace bigger circles in the same time.
Heavier particles have larger r and longer T at the same v and B.
If v has both parallel and perpendicular components: helical motion (circle plus drift).

Magnetic fields from currents

Biot-Savart for a long wire, the centre of a circular coil, and inside a solenoid.

Straight wire

Field of an infinite straight wire

B = mu_0 I over 2 pi r. Field falls inversely with distance.

Magnetic field at perpendicular distance r from a long straight wire. Direction by the right-hand rule (curl fingers around the wire in the direction of current).

Current I: 5 A

Distance r: 5.0 cm

Magnetic field B

20.00 µT

B = \frac{μ _{0} I}{2 π r}

Try this

Doubling I doubles B. Doubling r halves B (1/r dependence).
5 A at 5 cm gives about 20 µT (compare to Earth's field around 50 µT).
Field forms concentric circles around the wire. Right-hand rule for direction.

Circular coil

Field of a circular coil (centre and axis)

At the centre, B = mu_0 N I over 2 R. On the axis, the formula adds an (R² + x²) term.

Field at the centre and on the axis of a circular coil with N turns. At the centre, x = 0 and the formula simplifies.

Current I: 5 A

Radius R: 5.0 cm

Turns N: 50

Distance from centre x: 0.0 cm

B at centre (x = 0)

3.142 mT

B_{0} = \frac{μ _{0} N I}{2 R}

B on axis at x

3.142 mT

B = \frac{μ _{0} N I R ^{2}}{2 ( R ^{2} + x ^{2} ) ^{3/2}}

Try this

At centre: B is maximum on the axis.
Far away (x much greater than R): B falls as 1/x³ (looks like a magnetic dipole).
Doubling N doubles B. Doubling R at fixed I and N halves B at the centre.

Solenoid

Magnetic field inside a solenoid

B = mu_0 n I. Uniform inside, zero outside.

Inside a long ideal solenoid, the field is uniform along the axis and equal to mu_0 n I. At the end of a finite solenoid, B is half the value at the middle.

Turns per metre n: 1000

Current I: 5 A

B inside (middle)

6.283 mT

B = μ_{0} n I

B at end of solenoid

3.142 mT

B_{end} = \frac{1}{2} μ_{0} n I

Try this

Field is independent of cross-section area or radius (for an ideal long solenoid).
1000 turns/m at 5 A: B about 6.3 mT, more than 100x Earth's field.
Outside a long solenoid: B is essentially zero.
Solenoid is the magnetic analog of a parallel-plate capacitor (uniform field inside, zero outside).

Force and torque

Force between two parallel wires, plus the torque on a current loop in a uniform B.

Parallel wires

Force between two parallel current-carrying wires

F per unit length = mu_0 I_1 I_2 over 2 pi d. Attract or repel based on relative current direction.

Two parallel wires carrying currents. Same direction: they attract. Opposite directions: they repel.

I₁: 5 A

I₂: 5 A

Separation d: 10.0 cm

Force per unit length

5.000e-5 N/m

Attractive

\frac{F}{L} = \frac{μ _{0} I _{1} I _{2}}{2 π d}

Try this

I₁ = I₂ = 1 A, d = 1 m: force per length = 2 × 10⁻⁷ N/m. This is the OLD definition of the ampere.
Halving d doubles the force per metre.
Attractive when currents are parallel. Repulsive when antiparallel.

Torque on loop

Torque on a current loop

τ = m × B = N I A B sin θ. The principle behind moving-coil meters and electric motors.

Torque on a current loop in a uniform magnetic field. Used in galvanometers and electric motors. Torque tries to align m with B.

Turns N: 20

Current I: 2.00 A

Area A: 100 cm²

B: 0.50 T

θ between m and B: 60°

Torque τ

1.73e-1 N·m

τ = m B sin θ

Magnetic moment m

4.00e-1 A·m²

m = N I A

Try this

θ = 0° (m parallel to B): torque = 0, stable equilibrium.
θ = 90°: maximum torque, m B.
In a galvanometer, a spring provides a restoring torque proportional to deflection. At equilibrium, m B sin θ = c θ.

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