Related questions with answers

A cosmic-ray electron moves at $7.5 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s }$ perpendicular to Earth’s magnetic field at an altitude where the field strength is $1.0 \times 10 ^ { - 5 } \mathrm { T }$ . What is the radius of the circular path the electron follows?

An alpha-particle $\left( m = 6.64 \times 10 ^ { - 27 } \mathrm { kg }, q = 3.2 \times 10 ^ { - 19 } \mathrm { C } \right)$ moving with a velocity $\vec { \mathbf { v } } = ( 2.0 \hat { \mathbf { i } } - 4.0 \hat { \mathbf { k } } ) \times 10 ^ { 6 } \mathrm { m } / \mathrm { s }$ enters region where $\vec { \mathbf { E } } = ( 5.0 \hat { \mathbf { i } } - 2.0 \hat { \mathbf { j } } ) \times 10 ^ { 4 } \mathrm { V } / \mathrm { m }$ and $\vec { \mathbf { B } } = ( 1.0 \hat { \mathbf { i } } + 4.0 \hat { \mathbf { k } } ) \times 10 ^ { - 2 } \mathrm { T }$ . What is the initial force on it?

(a) A dc power line for a light-rail system carries 1000 A at an angle of $30.0 ^ { \circ }$ to Earth’s $5.0 \times 10 ^ { - 5 } \mathrm { T }$ field. What is the force on a 100-m section of this line? (b) Discuss practical concerns this presents, if any.