Moving Charges and Magnetism [INCOMPLETE]

In Progress

What is Biot-Savart’s Law used for?

Vector form of Biot-Savart’s Law?

What is the unit of magnetic field?

unit of B = Newton second / (coulomb metre) = Ns/Cm. This unit is called tesla ( T ).

1 gauss = 10^–4 tesla

What is μ₀?

permeability

What direction is magnetic field in relation to current-carrying wire and distance from wire?

perpendicular to both

What is the relationship between μ_r, μ_m and μ₀?

What is the dimensional formula of Magnetic Field?

[B] = [MA^-1T^-2]

What is the formula for magnetic field surrounding thin, straight, current-carrying conductor?

a is distance from wire

What is the formula for magnetic field surrounding infinite thin, straight, current-carrying conductor?

d = distance from wire

What is the formula for magnetic field surrounding semi-infinite thin, straight, current-carrying conductor?

d = distance from wire

What is the formula for magnetic field surrounding semi-infinite thin, straight, current-carrying conductor where θ=0?

d = distance from wire

What is the formula for magnetic field surrounding thin, straight, current-carrying conductor when perpendicular point lies outside the length of the wire?

What is the formula for magnetic field at the axis of a current-carrying loop or ring?

Where r is the radius of the loop and x is the distance along the axis from the centre of the loop.

If there is a current-carrying loop with number of turns ‘n’, what is the magnetic field at the centre of the loop?

In case of a current-carrying loop, at a point far far away from the centre (x> > > >R), comment on the relationship between the magnetic field and the distance from the loop?

In case of a current-carrying loop, at a point along the axis very very close to the centre (x < < < R), What is the ratio of change in magnetic field to the magnetic field at the centre of the loop?

What is Ampere’s Circuital Law formula?

What is the formula for magnetic field outside or on the surface of an infinite current-carrying wire with non-zero thickness?

Where R is the distance from the centre of the wire to that point.

What is the formula for magnetic field inside an infinite hollow current-carrying wire?

0

What is the formula for magnetic field inside an infinite solid current-carrying wire?

Where

r = distance from centre of wire to that point

R = radius of wire

How will you approach cavity problems when finding magnetic field outside the cavity?

Find Magnetic field due to solid body and magnetic field due to cavity separately, then subtrace the latter from the former.

What is the formula for magnetic field inside a solid infinite cylindrical current-carrying wire in terms of current density?

where

r = distance from centre of wire to that point

R = radius of wire

How will you approach cavity problems when finding magnetic field inside the cavity?

where

r_A = distance from centre of solid body to the point

r_B = distance from centre of cavity to the point

and direction of magnetic field is given by

How do you find the direction of magnetic field inside the cavity?

where ‘l’ is the line joining the centre of the body to the centre of the cavity.

B outside a solenoid is ________ (negligible/gligible)

negligible

What is the formula for magnetic field inside an infinite-length solenoid at its centre?

where n is the number of turns per unit length

What is the formula for magnetic field inside a finite-length solenoid?

where n is the number of turns per unit length

What is the formula for magnetic field inside an infinite-length solenoid at its axial end point?

where n is the number of turns per unit length

What is the magnetic field inside a toroid?

where:

n = number of turns per unit length

N = number of turns

n = N/L = N/circumference of circle

What is the formula for magnetic field due to a moving charge in both scalar and vector form?

What is Lorentz’s Law?

If there is a maoving charge, it will develop a magnetic field around it.

What is the formula for the magnetic force experienced by a moving charge in an external magnetic field?

where:

q = charge of particle

v = velocity of particle

B = external field

Which of the following statements is false?

1. Work done by magnetic force is 0.

2. F_m only acts on moving charges.

3. F_m changes the kinetic energy of a moving charge.

4. F_m always acts perpendicular to velocity of moving charge.

3. F_m changes the kinetic energy of a moving charge.

This is false, F_m does not change the kinetic energy of a moving charge. as it never changes the speed of the particle.

When a magnetic field is perpendicular to velocity of a charge, the charge moves in a circle.

What is the formula for radius of this circle?

When a magnetic field is perpendicular to velocity of a charge, the charge moves in a circle.

What is the formula for time period of this circular movement?

When a magnetic field is perpendicular to velocity of a charge, the charge moves in a circle.

What is the formula for frequency of this circular movement?

When a magnetic field is perpendicular to velocity of a charge, the charge moves in a circle.

What is the formula for angular velocity (ω) of this circular movement?

Inside a magnetic separator, when the diameter of the separator is greater than the radius of circle of movement (d>r), what is the time it takes for a charged particle projected perpendicular to it to exit the separator?

Inside a magnetic separator, when the diameter of the separator is less than the radius of circle of movement (d<r), what is the time it takes for a charged particle projected perpendicular to it to exit the separator?

If the velocity of a particle and the external magnetic field are at some angle,

What is the formula for radius of the helical movement?

If the velocity of a particle and the external magnetic field are at some angle,

What is the formula for time period of the helical movement?

If the velocity of a particle and the external magnetic field are at some angle,

What is the formula for pitch of the helical movement?

(pitch = distanced travelled by the particle perpendicular to circular shape, in time period T)

if velocity v of a particle and external electric and magnetic fields E and B are all collinear, what is the total force exerted on the particle?

equal to the electric force, as magnetic force is 0.

What sort of movement will happen if a particle moves with velocity v perpendicular to both external electric field and external magnetic field (which are in the same direction)?

the particle will forlow a helical path but with continuously increasing pitch length.

When velocity of a charged particle, electric field, and magnetic field are all perpendicular to each other, what is the net force on the particle? what is the velocity of the particle?

the net force is 0, so the net acceleration is 0.

v=\frac{E}{B}

What is the formula for force experienced by a current-carrying wire in an external magnetic field? (both scalar and vector forms)

What is the formula for force experienced by a curved current-carrying wire in an external magnetic field? (vector form)

For a closed loop, the net magnetic force in a constant magnetic field is zero. true or false?

true

What is the formula for force per unit length exerted on one infinite-length current-carrying wire by another infinite-length current-carrying wire?

What is the nature of the force, when the currents flow in the same direction?

What is the nature of the force, when the currents flow in opposite directions?

where d is the perpendicular distance between the two wires.

when the currents flow in the same direction, the force is attractive in nature.

when the currents flow in opposite directions, the force is repulsive in nature.

What is the formula for force exerted on one moving charge by another moving charge?

What is the nature of the force?

where d is the perpendicular distance between the two particles.

The force is attractive in nature.

For two charged particles moving with their own velocities, which is greater: the magnetic forces between them or the electric forces between them?

F_{M}<<<F_{E}

What is the torque on a loop of conducting wire when the plane of the loop is perpendicular to the magnetic field?

0

What is the formula for torque on a conducting loop of wire placed in a uniform magnetic field? (both scalar and vector forms)

What is magnetic dipole moment formula?

What is the energy needed to rotate a loop in a constant external magnetic field by θ?

What is the energy stored in a loop in a constant external magnetic field for any θ? (where θ is the angle between the magnetic field and the normal vector to the plane of the loop)