Of the charge $$Q$$ on a tiny sphere, a fraction $$\alpha$$ is to be transferred to a second, nearby sphere. The spheres can be treated as particle. smaller
The two charges are $$q= \alpha Q$$ (where $$\alpha$$ is a pure number presumably less than $$1$$ and greater than zero) and $$Q-q=(1- \alpha)Q$$. Thus,Eq. gives$$F=\dfrac{1}{4\ \pi \varepsilon _0}\dfrac{(\alpha Q)((1- \alpha)Q)}{d^2}=\dfrac{Q^2 \alpha(1- \alpha)}{4\ \pi \varepsilon _0 d^2}$$.
The graph below, of $$F$$ versus $$\alpha$$, has been scaled so that the maximum is $$1$$. In actuality,the maximum value of the force is $$F_{max}=Q^2/16 \pi \varepsilon _0 d^2$$.
Seeking the half-height points on the graph is difficult without grid or some of the special tracing features found in a verity of modern calculators. It is not difficult to algebraically solve for the half-height point (this involves the use of the quadratic formula ). The results are
$$\alpha_1=\dfrac{1}{2}\left(1-\dfrac{1}{\sqrt{2}}\right) \approx 0.15$$ and $$\alpha_1=\dfrac{1}{2}\left(1+\dfrac{1}{\sqrt{2}}\right) \approx 0.85$$
Thus, the smaller value of $$\alpha$$ is $$\alpha_1=0.15$$
A uniformly charged ring of radius $$3a$$ and total charge $$q$$ is placed in xy-plane centred at origin. A point charge $$q$$ is moving towards the ring along the z-axis and has speed $$u$$ at $$z-4a$$. The minimum value of $$u$$ such that it crosses the origin is :
In the return stroke of a typical lighting bolt, current of $$2.5\times 10^4\ A$$ exist for $$20\ \mu s$$. How much charge is transferred in this event?
Of the charge $$Q$$ on a tiny sphere, a fraction $$\alpha$$ is to be transferred to a second, nearby sphere. The spheres can be treated as particle. larger values of $$\alpha$$ that put $$F$$ at half the maximum magnitude?
If a cat repeatedly rubs against your cotton slacks on a dry day, the charge transfer between the cat hair and the cotton can leave you with an excess charge of $$-2.00 \mu C$$. In that spark, do electrons flow from you to the faucet or vice varsa?
Which of the following sets has different dimensions?
A small charged particle of mass $$m$$ and charge $$q$$ is suspended by an insulated thread in front of a very large conducting charged sheet of uniform surface density of charge $$\sigma$$. The angle made by the thread with the vertical in equilibrium is
Consider the situation depicted in the adjacent figure. The work done in taking a point charge from $$P$$ to $$A$$ is $$W_A$$, from $$P$$ to $$B$$ is $$W_B$$ and from $$P$$ to $$C$$ is $$W_C$$. Therefore,
A charge $$Q$$ is fixed at a distance $$d$$ in front of an infinite metal plate. The lines of force are represented by
Two force point charges $$+q$$ and $$+4q$$ are a distance $$\ell$$ apart. A third charge $$q_1$$ is so placed that the entire system is in equilibrium. Find the location, magnitude and sign of the third charge.
Five point charges, each of charge $$+q$$ are placed on five vertices of a regular hexagon of side $$h$$ as shown in the figure. Then