Solveeit Logo
Login

Question

Question: An electron having charge \(2 \times 10 ^ { - 1 }\) tesla in a circular orbit. The force acting on e...

An electron having charge 2×10−12 \times 10 ^ { - 1 } tesla in a circular orbit. The force acting on electron and the radius of the circular orbit will be

A

12.8×10−13 N,1.1×10−4 m12.8 \times 10 ^ { - 13 } \mathrm {~N} , 1.1 \times 10 ^ { - 4 } \mathrm {~m}

B

1.28×10−14 N,1.1×10−3 m1.28 \times 10 ^ { - 14 } \mathrm {~N} , 1.1 \times 10 ^ { - 3 } \mathrm {~m}

C

1.28×10−13 N,1.1×10−3 m1.28 \times 10 ^ { - 13 } \mathrm {~N} , 1.1 \times 10 ^ { - 3 } \mathrm {~m}

D

1.28×10−13 N,1.1×10−4 m1.28 \times 10 ^ { - 13 } \mathrm {~N} , 1.1 \times 10 ^ { - 4 } \mathrm {~m}

Answer

1.28×10−13 N,1.1×10−4 m1.28 \times 10 ^ { - 13 } \mathrm {~N} , 1.1 \times 10 ^ { - 4 } \mathrm {~m}

Explanation

Solution

F = evB=1.6×10−19×4×106×2×10−1= 1.6 \times 10 ^ { - 19 } \times 4 \times 10 ^ { 6 } \times 2 \times 10 ^ { - 1 }

Also mv2r=evB⇒r=mveB\frac { m v ^ { 2 } } { r } = e v B \Rightarrow r = \frac { m v } { e B }

⇒r=9×10−31×4×1061.6×10−19×2×10−1=1.1×10−4 m\Rightarrow r = \frac { 9 \times 10 ^ { - 31 } \times 4 \times 10 ^ { 6 } } { 1.6 \times 10 ^ { - 19 } \times 2 \times 10 ^ { - 1 } } = 1.1 \times 10 ^ { - 4 } \mathrm {~m}