Answer:
The height of the image will be "1.16 mm".
Explanation:
The given values are:
Object distance, u = 25 cm
Focal distance, f = 1.8 cm
On applying the lens formula, we get
⇒ ![\frac{1}{v} -\frac{1}{u} =\frac{1}{f}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bv%7D%20-%5Cfrac%7B1%7D%7Bu%7D%20%3D%5Cfrac%7B1%7D%7Bf%7D)
On putting estimate values, we get
⇒ ![\frac{1}{v} -\frac{1}{(-25)} =\frac{1}{1.8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bv%7D%20-%5Cfrac%7B1%7D%7B%28-25%29%7D%20%3D%5Cfrac%7B1%7D%7B1.8%7D)
⇒ ![\frac{1}{v} =\frac{1}{1.8} -\frac{1}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bv%7D%20%3D%5Cfrac%7B1%7D%7B1.8%7D%20-%5Cfrac%7B1%7D%7B25%7D)
⇒ ![v=1.94 \ cm](https://tex.z-dn.net/?f=v%3D1.94%20%5C%20cm)
As a result, the image would be established mostly on right side and would be true even though v is positive.
By magnification,
and
⇒ ![\frac{v}{u} =\frac{h_{1}}{h_{0}}](https://tex.z-dn.net/?f=%5Cfrac%7Bv%7D%7Bu%7D%20%3D%5Cfrac%7Bh_%7B1%7D%7D%7Bh_%7B0%7D%7D)
⇒ ![\frac{1.94}{25}=\frac{{h_{1}}}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B1.94%7D%7B25%7D%3D%5Cfrac%7B%7Bh_%7B1%7D%7D%7D%7B15%7D)
⇒ ![{h_{1}}=1.16 \ mm](https://tex.z-dn.net/?f=%7Bh_%7B1%7D%7D%3D1.16%20%5C%20mm)
Answer:
(a) the force is 8.876 N
(b) the magnitude of each charge is 4.085 μC
Explanation:
Part (a)
Given;
coulomb's constant, K = 8.99 x 10⁹ N.m²/C²
distance between two charges, r = 10 cm = 0.1 m
force between the two charges, F = 15 N
when the distance between the charges changes to 13 cm (0.13 m)
force between the two charges, F = ?
Apply Coulomb's law;
![F = \frac{Kq_1q_2}{r^2} \\\\let \ Kq_1q_2 = C\\\\F =\frac{C}{r^2} \\\\C = Fr^2\\\\F_1r_1^2 = F_2r_2^2\\\\F_2 =\frac{F_1r_1^2}{r_2^2} \\\\F_2 = \frac{15*0.1^2}{0.13^2} \\\\F_2 = 8.876 \ N](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7BKq_1q_2%7D%7Br%5E2%7D%20%5C%5C%5C%5Clet%20%5C%20Kq_1q_2%20%3D%20C%5C%5C%5C%5CF%20%3D%5Cfrac%7BC%7D%7Br%5E2%7D%20%5C%5C%5C%5CC%20%3D%20Fr%5E2%5C%5C%5C%5CF_1r_1%5E2%20%3D%20F_2r_2%5E2%5C%5C%5C%5CF_2%20%3D%5Cfrac%7BF_1r_1%5E2%7D%7Br_2%5E2%7D%20%5C%5C%5C%5CF_2%20%3D%20%5Cfrac%7B15%2A0.1%5E2%7D%7B0.13%5E2%7D%20%5C%5C%5C%5CF_2%20%3D%208.876%20%5C%20N)
Part (b)
the magnitude of each charge, if they have equal magnitude
![F = \frac{KQ^2}{r^2}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7BKQ%5E2%7D%7Br%5E2%7D)
where;
F is the force between the charges
K is Coulomb's constant
Q is the charge
r is the distance between the charges
![F = \frac{KQ^2}{r^2} \\\\Q = \sqrt{\frac{Fr^2}{K} } \\\\Q = \sqrt{\frac{15*(0.1)^2}{8.99*10^9} } = 4.085 *10^{-6} \ C\\\\Q = 4.085 \ \mu C](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7BKQ%5E2%7D%7Br%5E2%7D%20%5C%5C%5C%5CQ%20%3D%20%5Csqrt%7B%5Cfrac%7BFr%5E2%7D%7BK%7D%20%7D%20%5C%5C%5C%5CQ%20%3D%20%20%5Csqrt%7B%5Cfrac%7B15%2A%280.1%29%5E2%7D%7B8.99%2A10%5E9%7D%20%7D%20%3D%204.085%20%2A10%5E%7B-6%7D%20%5C%20C%5C%5C%5C%5CQ%20%3D%204.085%20%5C%20%5Cmu%20C)
they absorb sunlight and turn it into glucose I think.