an electron enters a region with velocity v=4i + 6j m/s where an electric field where i= 2i + 3j +6k and magnetic field 2i + 3j t are present what is the magnitude of force experience by electron

Asked by archs370 | 27th May, 2021, 10:47: AM

Expert Answer:

Velocity of electron , begin mathsize 14px style v with rightwards arrow on top end style = ( 4 begin mathsize 14px style i with hat on top end style + 6 begin mathsize 14px style j with hat on top end style ) m/s 
Electric field , begin mathsize 14px style E with rightwards arrow on top end style = ( 2 begin mathsize 14px style i with hat on top end style + 3 begin mathsize 14px style j with hat on top end style + 6 begin mathsize 14px style k with hat on top end style ) N/C
Magnetic field Induction ,  begin mathsize 14px style B with rightwards arrow on top end style = ( 2 begin mathsize 14px style i with hat on top end style + 3 begin mathsize 14px style j with hat on top end style ) T 
 If we observe the given velocity  begin mathsize 14px style v with rightwards arrow on top end style and  begin mathsize 14px style B with rightwards arrow on top end style , we see that  begin mathsize 14px style v with rightwards arrow on top end style | |  begin mathsize 14px style B with rightwards arrow on top end style 
Hence (  begin mathsize 14px style v with rightwards arrow on top end style  ×  begin mathsize 14px style B with rightwards arrow on top end style ) force is zero . 
Hence only electric field is acting on electron to give force F = q begin mathsize 14px style E with rightwards arrow on top end style , where q is charge on electron
F = 1.602 × 10-19 × ( 2 begin mathsize 14px style i with hat on top end style + 3 begin mathsize 14px style j with hat on top end style + 6 begin mathsize 14px style k with hat on top end style )  N
Magnitude of force = 1.602 × 10-19 ×  { 2 × 2 + 3 × 3 + 6 × 6 }1/2 = 1.121 × 10-18 N

Answered by Thiyagarajan K | 27th May, 2021, 11:13: AM

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