Show that for a straight conductor, the magnetic field
\(\overset { \rightarrow }{ B } =\frac { { \mu }_{ ° }I }{ 4\pi a } (cos\varphi _{ 1 }-cos\varphi _{ 2 })\hat { n } \)
\(=\frac { { \mu }_{ ° }I }{ 4\pi a } (sin{ \theta }_{ 1 }+sin{ \theta }_{ 2 })\hat { n } \)

Compute the magnitude of the magnetic field of a long, straight wire carrying a current of 1 A at distance of 1m from it. Compare it with Earth’s magnetic field.

A particle of charge q moves with velocity\(\vec { v } \) along positive y-direction in a magnetic field \(\vec { B } \) .Compute the Lorentz force experienced by the particle
(a) when magnetic field is along positive y - direction
(b) when magnetic field points in positive z - direction
(c) when magnetic field is in zy - plane and making an angle θ with velocity of the particle. Mark the direction of magnetic force in each case

An electron moving perpendicular to a uniform magnetic field 0.500 T undergoes circular motion of radius 2.50 mm. What is the speed of electron?

Two singly ionized isotopes of uranium \(_{ 92 }^{ 235 }{ U \ and \ _{ 92 }^{ 238 }{ U } }\) (isotopes have same atomic number but different mass number) are sent with velocity 1.00 x 10⁵ m s^–1 into a magnetic field of strength 0.500 T normally. Compute the distance between the two isotopes after they complete a semi-circle. Also, compute the time taken by each isotope to complete one semi-circular path. (Given: masses of the isotopes: m₂₃₅ = 3.90 x 10^–25 kg and m₂₃₈ = 3.95 x 10^–25 kg)