Two metal spheres, each of mass 0.3 kg, are oppositely charged by an electrostat

Question

Two metal spheres, each of mass 0.3 kg, are oppositely charged by an electrostatic generator. Each is attached to an identical insulating string and suspended from the ceiling, as shown at right. Sphere A is negative with a charge magnitude three times that on sphere B. They attract each other and hang with separation 0.4 m. The length of the string from a point of support to the center of a ball is 2.5 m. Draw the electric field lines for this arrangement. What is the electrostatic force on each sphere? 0.355 N What is the charge on each sphere? 1.45 mu C, -4.34 mu C The two spheres are briefly connected by a copper wire. What is the final charge on each sphere? -1.45 mu C What now is the separation distance between the two spheres? 1.03 m Two charged objects are connected to a spring with force constant k = 500 N/m and unstretched length L_o = 50 cm. The magnitude of each charge is the same. The charge on the left is fixed to the wall, but the charge on the right is free to move on the frictionless surface (stretching or compressing the spring) until it reaches equilibrium. If the objects are 1.0 m apart at equilibrium, what is the magnitude of each charge? 167 mu C If the objects have 30-mu C opposite charges, what is their separation at equilibrium? 0.259 m, 0.397 m If the objects have 30-mu C like charges, what is their separation at equilibrium? 0.553 m

Explanation / Answer

Question 36:

Charge on Sphere a = - 3q

Charge on Sphere b = q

Electrostatic Force, F = k*q*3q/r^2

As they have same mass and Same Force will be acting on each other, they wil make same anlge wrt Vertical.

Angle = sin^-1(0.3/2.5)

Angle = 6.9

Now, T*cos(6.9) = 0.3*9.8

T = 2.96 N

Electrostatic force on each sphere, = T*sin(6.9) = 2.96 * sin(6.9)

Electrostatic force on each sphere, = 0.355 N

Question 37:

k*q*3q/r^2 = 0.355

(9.0*10^9 * 3q^2)/0.4^2 = 0.355

q = 1.45 * 10^-6 C

q = 1.45 uC

Charge on Sphere A, = - 4.34 uC

Charge on Sphere B, = 1.45 uC

Question 38:

When they are connected together,

Final Charge on each sphere, = (q-3q)/2 = -q

Final Charge on each sphere, = - 1.45 uC

Question 39:

Now they will Repel each other, F = k*q^2/r^2

T*cos() = m*g

T*sin() = k*q^2/r^2

tan() = k*q^2/r^2/ m*g

(r-1)/2/sqrt( -((r-1)/2)^2 + 2.5^2) = (9.0*10^9 * (1.35*10^-6)^2)/(r^2*0.3*9.8)

r = 1.025 m

r = 1.03 m

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