The fallowing spheres are touched in this order...
step 1: K & L
step 2: K & M
step 3: L & M
the final charges on the three spheres are
[K = +x/2] [L = -x/4] [M = -X/4]
thanks
To determine the final charges on each sphere, you need to apply the principle of charge conservation. Charge conservation states that the total charge of an isolated system remains constant. In this case, the initial total charge of the system is zero because there is no mention of initial charges on any of the spheres.
Let's analyze each step:
Step 1: When spheres K and L touch, charge is transferred between them. To find the charge transferred, you can apply the principle of charge conservation. Since the total charge is zero initially, it should be zero after the transfer as well.
Initially, K has a charge of +x/2, and L has a charge of -x/4. To have a net charge of zero, the transferred charge from K to L should be half of the initial charge of K plus half of the initial charge of L:
Transferred charge = (1/2)(+x/2) + (1/2)(-x/4) = x/4 - x/8 = x/8
After the transfer, the charges on the spheres are:
[K = +x/2 - x/8 = 4x/8 - x/8 = 3x/8]
[L = -x/4 + x/8 = -2x/8 + x/8 = -x/8]
Step 2: When spheres K and M touch, charge is transferred again. To find the transferred charge, we can use the same principle of charge conservation.
Initially, K has a charge of 3x/8, and M has a charge of -x/4. The transferred charge from K to M should be:
Transferred charge = (1/2)(3x/8) + (1/2)(-x/4) = (3/16)x - (1/8)x = (3/16 - 1/8)x = (3/16 - 2/16)x = (1/16)x
After the transfer, the charges on the spheres are:
[K = 3x/8 - (1/16)x = (12x - x)/32 = 11x/32]
[M = -x/4 + (1/16)x = (-8x + x)/16 = -7x/16]
Step 3: When spheres L and M touch, charge is transferred once more. We can determine the transferred charge using the charge conservation principle.
Initially, L has a charge of -x/8 and M has a charge of -7x/16. The transferred charge from L to M should be:
Transferred charge = (1/2)(-x/8) + (1/2)(-7x/16) = (-1/16)x + (-7/32)x = (-2/32)x + (-7/32)x = (-9/32)x
After the transfer, the charges on the spheres are:
[L = -x/8 - (-9/32)x = -4x/32 + 9x/32 = 5x/32]
[M = -7x/16 + (-9/32)x = -14x/32 - 9x/32 = -23x/32]
Final charges on the spheres are:
K = 11x/32
L = 5x/32
M = -23x/32
Therefore, the final charges are:
[K = 11x/32] [L = 5x/32] [M = -23x/32]