Problem 3: A point charge P is b = 7.5 m above the center of a uniformly charged ring Z-axis of radius a = 0.24 m sitting in the xy plane with charge Q = 6.5 ?C Randomized Variables b=7.5 m a 0.24 m (o,0.b) X-axi (a,0.0) Otheexpertta.com Part (a) Calculate the z component of the electric field at P in newtons per coulomb Numeric : Anumeric value is expected and not an expression Part (b) Calculate the x and y components of the electric field at P in newtons per coulomb Numeric : A numeric value is expected and not an expression Ex-Ey- Part (c) Assume b is very largc. Now if b doubles, what happens to the magnitude of thc Electric Ficld? MultipleChoice: 1) The electrical field at P doubles 2) The electrical field at P quadruples 3) The electrical field at P becomes a quarter of its previous strength 4) None of thesc 5) The electrical field at P is unchanged 6) The electrical field at P becomes half of its previous strength Solution for any infinitisimal charge dq, making an angle with Z axis theta , the electric field\'s z component is given by k*dq*cos(theta)/(b^2+a^2) cos(theta)=b/sqrt(b^2+a^2) substituting, we get electric field component = k*b*dq/(b^2+a^2)^1.5 integrating from q=0 to q=Q, we get electric field component = k*b*Q/(b^2+a^2)^1.5 putting all the values, we get electric field\'s z component = 1038.40 N/C b) as the ring of charge is symmetrical, all other components of electric field on the axis will be 0. hence x component = 0 y component = 0 c) if b is very large, the electric field becomes k*b*Q/b^3 = k*Q/b^2 now if b doubles, the electric field strength will become a quarter of previous value. Hence, 3rd option is correct. .

1. Problem 3: A point charge P is b = 7.5 m above the center of a uniformly charged ring Z-axis of
radius a = 0.24 m sitting in the xy plane with charge Q = 6.5 ?C Randomized Variables b=7.5 m
a 0.24 m (o,0.b) X-axi (a,0.0) Otheexpertta.com Part (a) Calculate the z component of the
electric field at P in newtons per coulomb Numeric : Anumeric value is expected and not an
expression Part (b) Calculate the x and y components of the electric field at P in newtons per
coulomb Numeric : A numeric value is expected and not an expression Ex-Ey- Part (c) Assume b
is very largc. Now if b doubles, what happens to the magnitude of thc Electric Ficld?
MultipleChoice: 1) The electrical field at P doubles 2) The electrical field at P quadruples 3) The
electrical field at P becomes a quarter of its previous strength 4) None of thesc 5) The electrical
field at P is unchanged 6) The electrical field at P becomes half of its previous strength
Solution
for any infinitisimal charge dq, making an angle with Z axis theta , the electric field's z
component is given by k*dq*cos(theta)/(b^2+a^2)
cos(theta)=b/sqrt(b^2+a^2)
substituting, we get
electric field component = k*b*dq/(b^2+a^2)^1.5
integrating from q=0 to q=Q, we get
electric field component = k*b*Q/(b^2+a^2)^1.5
putting all the values, we get electric field's z component = 1038.40 N/C
b) as the ring of charge is symmetrical, all other components of electric field on the axis will be
0.
hence x component = 0
y component = 0
c) if b is very large, the electric field becomes

2. k*b*Q/b^3 = k*Q/b^2
now if b doubles, the electric field strength will become a quarter of previous value.
Hence, 3rd option is correct.