Given that the electric field in an xy plane produced by apostively charged part

Question

Given that the electric field in an xy plane produced by apostively charged particle is    E = 7.2(4.0 i + 3.0 j)N/C at the point(3.0,3.0)cm and is 100i N/C at the point (2.0,0)cm
What are the (a) x and (b) y coordinates of the particle? (c)What is that charge of the particle?


I am very confused with the answers given in the book (as well asthe one posted on the cramster site) Could anyone pleaseplease help walk me thought the steps/and or theory?

Thanks so much for your time!!




Given that the electric field in an xy plane produced by apostively charged particle is    E = 7.2(4.0 i + 3.0 j)N/C at the point(3.0,3.0)cm and is 100i N/C at the point (2.0,0)cm
What are the (a) x and (b) y coordinates of the particle? (c)What is that charge of the particle?


I am very confused with the answers given in the book (as well asthe one posted on the cramster site) Could anyone pleaseplease help walk me thought the steps/and or theory?

Thanks so much for your time!!

Explanation / Answer

   Given      E1   =   7.2* (4.0 i   +   3.0j)      N/C                          =   (28.8i   +   21.6j)   N/C            at   (3.0,3.0)       x component of  E at (3.0,3.0)  (Ex)1    =   28.8 i      N/C         -------(1)       y component of E at (3.0,3.0)   (Ey)1   =   21.6j   N/C             ---------(2)                   E2   =   100i      N/C               at   (2.0,0)                     ----------(3)    E   =   {(1/40)* q / r2}r^    a.   At   (3.0,3.0),   r   =   x   =   3.0cm   =   0.03   m          (Ex)1   =   {(1/40)* q / (3 - x)2 * 10-4}i                    =   {q* 9 * 1013 / (3 -x)2} i         ------------(4)             (Ey)1   =   {(1/40)* q / (3 - y)2 * 10-4}j                    =   {q* 9 * 1013 / (3 -y)2}j         ------------(5)       From equation (1) and(4)       28.8   =   {q* 9 * 1013 / (3 -x)2}            ---------(6)    From equation (2) and (5)       21.6   =   {q* 9 * 1013 / (3 -y)2}            ---------(7)    Dividing equation (6) and (7)       (3 - x)2 / (3 -y)2   =   21.6 /28.8          (3 - x)/ (3 -y)   =   0.75                  --------(8)    2.   At (2.0, 0)       (Ex)2  =  {(1/40)* q / (2 - x)2 * 10-4}i                =   9* 1013 * q / (2 -x)2 i         -------(10)    Comparing with equation (3)    100   =   9 *1013 * q / (2 -x)2               --------(11)    Dividing equation (11) by (6)    100 /28.8   =   (3 - x)2 / (2 -x)2    (3 - x) / (2 -x)   =   3.47       3 -x   =   6.94 - 3.47 * x       x   =   (6.94- 3) / 2.47             =   1.59   cm    Substituting this value in (8)       (3 - 1.59) / (3 -y)   =   0.75       1.41   =   2.25- 0.75 * y       y   =   (2.25- 1.41) / 0.75          =   1.12 cm    Coordinates of chargedparticle      (x,y)   =   (1.59,1.12)   cm    (3 - x) / (2 -x)   =   3.47       3 -x   =   6.94 - 3.47 * x       x   =   (6.94- 3) / 2.47             =   1.59   cm    Substituting this value in (8)       (3 - 1.59) / (3 -y)   =   0.75       1.41   =   2.25- 0.75 * y       y   =   (2.25- 1.41) / 0.75          =   1.12 cm    Coordinates of chargedparticle      (x,y)   =   (1.59,1.12)   cm    b.   Substituting this valueof x in equation (11)          100   =   9* 1013 * q / (2 - 1.59)2          q   =   100* 0.1681 / 9 * 1013                =   1.87* 10-13   C                =   1.87* 10-13   C

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