A small metal sphere, A, carrying a charge of +15.0 C is at the origin (0, 0). A
ID: 1592322 • Letter: A
Question
A small metal sphere, A, carrying a charge of +15.0 C is at the origin (0, 0). An identical sphere, B, carrying a charge of -12.0 C is at (-3.0 cm, 0) and a third sphere, C, carrying +20.0 C is at (0, 4.0 cm).
(a) Find the total electrical force exerted on sphere A.
(b) Spheres B and C are touched together and then returned to their original locations. Now what is the force on sphere A?
(c) Let us view sphere A as a probe charge which we are using to measure the field due to spheres B and C. Use your result from part b) to find the electric field (note that this is a vector) at the origin.
(d) Sphere A is released so that it is free to move. It has a mass of 5.0 g and no forces other than the electrostatic forces found in b) act on it. What is its acceleration at the instant of release?
(e) A short time later will your answer from d) still be the correct acceleration for sphere A?
Explanation / Answer
a)
as the electric force between two charges is given as
F = k * q1 * q2/d^2
force on A due to B
FAB = 9*10^9 * 15 *10^-6 * 12 *10^-6/.03^2 (-i)
FAB = - 1.8 *10^3 N i
force on A due to C
FAC = 9*10^9 * 15 *10^-6 * 20*10^-6/.04^2 (-j)
FAC = - 1687.5 j
net electrical force = sqrt(FAC^2 + FAB^2)
net electrical force = sqrt(1687.5^2 + 1800^2)
net electrical force = 2467.3 N
the net electrical force acting on sphere A is 2467.3 N
b) if we touch the spehers B and C ,
charge on both will be same
q = (-12 + 20)/2 uC
q = 4 uC
force on A due to B
FAB = 9*10^9 * 15 *10^-6 * 4 *10^-6/.03^2 (i)
FAB = 600 N i
force on A due to C
FAC = 9*10^9 * 4 *10^-6 * 20*10^-6/.04^2 (-j)
FAC = - 450 j N
net electrical force = sqrt(600^2 + 450^2)
net electrical force = 750 N
the net force on A is 750 N
c) let the electric field is E
as force = q * E
750 = 15 *10^-6 * E
E = 5 * 10^7 N/C
the electric field at the origin is 5 * 10^7 N/C
d)
let the acceleration is a
using second equation of motion
750 = 0.005 * a
a = 1.5 *10^5 m/s^2
the acceleration of A will be 1.5 *10^5 m/s^2
e) No , as the charge A moves , the electrical force on sphere A will change and it's acceleration will also change
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