Three charged marbles are glued to a nonconducting surface and are placed in the

Question

Three charged marbles are glued to a nonconducting surface and are placed in the diagram as shown. The charges of each marble are q1 = 6.30 µC, q2 = 1.03 µC, and

q3 = 2.28 µC.

Marble q1 is a distance r1 = 3.00 cm to the left of the marble q2, while marble q3 is a distance r3 = 2.00 cm to the right of the marble q2, as shown. Calculate the magnitude of the electric field a distance r' = 1.00 cm to the left of the center marble.
_______________   N/C

Another marble is placed 1 cm to the left of the middle marble. If this new marble has a charge of

3.90 µC,

calculate magnitude and direction of the force on it.

___________________ N

___________________ N

Explanation / Answer

1. Given that :

charge on q1 = 6.3 x 10-6 C

charge on q2 = 1.03 x 10-6 C

charge on q3 = - 2.28 x 10-6 C

marble q1 has a distance, r1 = 3 cm = 0.03 m

marble q3 has a distance, r3 = 2 cm = 0.02 m

magnitude of the electric field at a distance, (r' = 0.01 m) to the left of the center marble which is given as ::

Using an equation, E = k Q / r2

Er' = k [q1 / (r1 - r')2 + q2 / (r')2 + q3 / (r3 + r1)2 { eq.1 }

where, k = constant = 9 x 109 Nm2/C2

inserting all these values in above eq.

Er' = (9 x 109 Nm2/C2) [(6.3 x 10-6 C) / (0.02 m)2 + (1.03 x 10-6 C) / (0.01 m)2 - (2.28 x 10-6 C) / (0.03 m)2]

Er' = (9 x 109 Nm2/C2) [(6.3 x 10-6 C) / (0.0004 m2) + (1.03 x 10-6 C) / (0.0001 m2) - (2.28 x 10-6 C) / (0.0009 m2)]

Er' = (9 x 109 Nm2/C2) [(15750 x 10-6 C/m2) + (10300 x 10-6 C/m2) - (2533.3 x 10-6 C/m2)

Er' = (9 x 109 Nm2/C2) (23516.7 x 10-6 C/m2)

Er' = 211650.3 x 103

Er' = 2.11 x 108 N/C

2. Another marble is placed (0.01 m) to the left of the middle marble.

magnitude of the force, F = q E                                                                      { eq.2 }

where, q = - 3.9 x 10-6 C

inserting the values in eq.2,

F = (3.9 x 10-6 C) (2.11 x 108 N/C)

F = 8.229 x 102 N

F = 823 N

And the direction is "to the left" or in -ve x-direction.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.