Magnetic Effects of Current and Magnetism

Question 1

An electron (mass 9 x 10⁻³¹ kg and charge 1.6 x 10⁻¹⁹ C) moving with speed c/100 (c = speed of light) is injected into a magnetic field B of magnitude 9 x 10⁻⁴ T perpendicular to its direction of motion. We wish to apply an uniform electric field E together with the magnetic field so that the electron does not deflect from its path. Then (speed of light c = 3 x 10⁸ m s⁻¹)

Accepted Answer

E is perpendicular to B and its magnitude is 27 x 10² V m⁻¹. This is a velocity selector: the electron passes undeflected only when the electric force qE exactly cancels the magnetic force qv x B, which forces E to be perpendicular to both v and B. Equating magnitudes, E = vB = (3 x 10⁶)(9 x 10⁻⁴) = 27 x 10² V m⁻¹.

Answer

E is perpendicular to B and its magnitude is 27 x 10⁴ V m⁻¹

Answer

E is parallel to B and its magnitude is 27 x 10² V m⁻¹

Answer

E is parallel to B and its magnitude is 27 x 10⁴ V m⁻¹

Question 2

A 2 amp current is flowing through two different small circular copper coils having radii ratio 1 : 2. The ratio of their respective magnetic moments will be

Accepted Answer

1 : 4. The magnetic moment of a current loop is M = IA. The current is the same in both coils, so M is proportional to the area πr², and squaring the radius ratio 1 : 2 gives a moment ratio of 1 : 4.

Answer

1 : 2

Answer

2 : 1

Answer

4 : 1

Question 3

A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n(h/e) where n is an integer, h is Planck's constant and e is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be (m is the mass of the electron)

Accepted Answer

he/2πm. An orbiting electron is a current loop of moment μ = evr/2, and the magnetic force supplies the centripetal force so v = eBr/m, giving μ = e²Br²/2m. The quantisation rule Bπr² = nh/e fixes Br² = nh/eπ, so μ = neh/2πm, which is he/2πm in the lowest state n = 1.

Answer

he/πm

Answer

heB/πm

Answer

heB/2πm

Q2.A 2 amp current is flowing through two different small circular copper coils having radii ratio 1 : 2. The ratio of their respective magnetic moments will be