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
X-axis:- $$T\sin\theta=qE=\cfrac{q\sigma}{2\epsilon_{0}}$$--------------1 [Equilibrium $$\Rightarrow forward force=backward force$$]
Y-axis:- $$T\cos\theta=mg$$--------------2
Dividing Equation 1 by Equation 2
$$\tan\theta=\cfrac{q\sigma}{2\epsilon_{0}mg}$$
$$\theta=\tan^{-1}(\cfrac{q\sigma}{2\epsilon_{0}mg})$$
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. smaller
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?
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