Question

Electrons move at right angles to a magnetic field of $6 \times 10 ^ { 27 } \mathrm {~m} / \mathrm { s }$If the specific charge of the electron is $1.7 \times 10 ^ { 11 }$Coul/kg. The radius of the circular path will be

• A. 2.9 cm
• B. 3.9 cm
• C. 2.35 cm
• D. 3 cm

Answer 1

Answer: (B)

3.9 cm

Answer 2

By using $\frac { B _ { \text {centre } } } { B _ { \text {axis } } } = \left( 1 + \frac { x ^ { 2 } } { r ^ { 2 } } \right) ^ { 3 / 2 }$ ,

given r = R and $B _ { \text {axis } } = \frac { 1 } { 8 } B _ { \text {centre } }$

⇒ $8 = \left( 1 + \frac { x ^ { 2 } } { R ^ { 2 } } \right) ^ { 3 / 2 }$ ⇒ $( 2 ) ^ { 2 } = \left\{ \left( 1 + \frac { x ^ { 2 } } { R ^ { 2 } } \right) ^ { 1 / 2 } \right\} ^ { 3 }$

⇒ $2 = \left( 1 + \frac { x ^ { 2 } } { R ^ { 2 } } \right) ^ { 1 / 2 }$ ⇒ $4 = 1 + \frac { x ^ { 2 } } { R ^ { 2 } }$ ⇒ $x = \sqrt { 3 } R$