Question

Three bees are oriented as shown in the figure. B, has 14 KC of charge, B2 has -5 HC of charge, and B, has 30 pC of charge. 5 cm 10 cmm What are the magnitude and direction of the electric field at B,? magnitude ow do you find the distance between B, and B,? How do you find the net electric field when multiple charges are present? Did you convert to SI units? direction 86 Does the sign of a charge affect its direction?0 counterclockwise from the x axis

Answer 1

Electric field is given by
E = kQ/R^2
We know that electric field due to positive charge is away from the positive charge and towards the negative charge.

from this we can see that electric field due to charge at B3 will be zero, because for that charge R = 0.

Electric field at B3 due to charge on B2 will be towards the left, since charge at B2 is negative, So

E2 = k*q2/R2^2

q2 = -5 uC = -5*10^-6 C

R2 = distance between B2 and B3 = 10 cm = 0.1 m

So,

E2 = 9*10^9*5*10^-6/0.1^2 = 4.5*10^6 N/C (towards -ve x-axis)

E2x = -4.5*10^-6 N/C

E2y = 0 N/C

Electric field at B3 due to charge on B1 will be towards the south of east, since charge at B1 is positive, So

E1 = k*q1/R1^2

q1 = 14 uC = 14*10^-6 C

R1 = distance between B1 and B3 = sqrt (10^2 + 5^2) cm = 11.2 cm = 0.112 m

So,

E1 = k*q1/R1^2

E1 = 9*10^9*14*10^-6/0.112^2 = 10.05*10^6 N/C

Direction of E1 will be

theta = arctan (5/10) = 26.56 deg below +x axis

E1x = E1*cos theta = 10.05*10^6*cos 26.56 deg = 9.0*10^6 N/C

E1y = -E1*sin theta = -10.05*10^6*sin 26.56 deg = -4.5*10^6 N/C

So Net electric field at B3 will be

E = Ex i + Ey j

E = (E1x + E2x) i + (E1y + E2y) j

E = (9.0*10^6 - 4.5*10^6) i + (-4.5*10^6 + 0) j

E = 4.5*10^6 i - 4.5*10^6 j

Magnitude of net electric field will be

|E| = sqrt ((4.5*10^6)^2 + (-4.5*10^6)^2) = 6.36*10^6 N/C

Direction of net electric field will be:

Direction = arctan (-4.5*10^6/(4.5*10^6)) = -45 deg

Direction = 45 deg clockwise of +x-axis = 360 - 45 = 315 deg Counter-clockwise of x-axis

Direction = 315 deg Counter-clockwise of x-axis

Please Upvote.

Comment below if you have any query.