Question

Calculate the force on an electron located at $P_2$ at $t=2.00s$

• A. $7.0\times {10}^{-11}N$
• B. $8.0\times {10}^{-21}N$
• C. $2.0\times {10}^{-15}N$
• D. $5.0\times {10}^{-20}N$

Answer 1

The correct option is B $8.0\times {10}^{-21}N$

$El=\frac{d\varphi }{dt}$

$E\left(2\pi r_2\right)=\pi R^2\cdot \frac{dB}{dt}$

$\therefore E=\frac{R^2}{2r_2}\left(\frac{dB}{dt}\right)$

$F=qE=\frac{e{R}^2}{2r_2}(6t^2-8t)$
Substituting the values we have

$F=\frac{(1.6\times {10}^{-19})(2.5\times {10}^{-2})}{2\times 5\times {10}^{-2}}[6{\left(2\right)}^2-8{\left(2\right)}^{}]=8.0\times {10}^{-21}N$

$⨂$ magnetic field at the given instant is increasing.Hence induced current in an imaginary circular loop passing through $P_2$ should produced. $⨀$ magnetic field. Or, current in this should be anticlockwise. Hence, electrons should move in clockwise direction. Or electron at $P_2$ should experience force in downward direction (perpendicular to $r_2$).