Electrostatics Question 241
Question: The electric field in a region is radially outward with magnitude $ E=A{\gamma _{0}} $ . The charge contained in a sphere of radius $ {\gamma _{0}} $ centered at the origin is [AMU 1999]
Options:
A) $ 1.77mm $
B) $ 3.51mm $
C) $ 1.77cm $
D) $ 3.51cm $
Show Answer
Answer:
Correct Answer: A
Solution:
Let an electron is projected towards the plate from the r distance as shown in fig.
It will not strike the plate if and only if KE £ e(E×r) (where E = Electric field due to charge plate $ =\frac{\sigma }{2{\varepsilon _{0}}} $ ) therefore $ r\ge \frac{KE}{eE} $ .
Hence minimum value of r is given by $ r=\frac{KE}{eE}=\frac{200eV}{e\times \frac{\sigma }{2{\varepsilon _{0}}}} $
$ =\frac{400\times 8.86\times {{10}^{-12}}}{2\times {{10}^{-6}}}=1.77mm $
