A charge cork ball of mass $$m$$ is suspended on a light string in the presence fo a uniform electric field as shown in the figure. When $$E=(A\hat{i}+B\hat{j})N{C}^{-1}$$, where $$A$$ and $$B$$ are positive numbers, the ball is in equilibrium at the $$\theta$$. Find (a) the charge on the ball and (b) the tension in the string.
A spherical conductor of radius 10 cm has a charge of $$3.2 \times 10^{-7} C$$ distributed uniformly. What is the magnitude of electric field at a point $$15 cm$$ from the centre of the sphere? $$\left(\dfrac{1}{4\pi \in_0} = 9\times 10^9 Nm^/C^2\right)$$
A conducting sphere of radius $$10\ cm$$ has an unknown charge. If the electric field $$20\ cm$$ from the centre of the sphere is $$1.5 \times 10^{3}\ N/C$$ and points radially inward, what is the net charge on the sphere?
A spherical conductor of radius 12 cm has a charge of $$1.6 \times 10^{-7}$$C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
Two charged conducting spheres of radii a and b are connected to each other by a wire. The ratio of electric fields at the surfaces of two spheres is:
A dielectric ball is polarized uniformly and statically. Its polarization equals $$P$$. Taking into account that a ball polarized in this way may be represented as a result of a small shift of all positive charges of the dielectric relative to all negative charges, (a) find the electric field strength $$E$$ inside the ball; (b) demonstrate that the field outside the ball is that of a dipole located at the centre of the ball, the potential of that field being equal to $$\varphi = p_{0}r/ 4\pi \epsilon_{0}$$, where $$p_{0}$$ is the electric moment of the ball, and $$r$$ is the distance from its centre.
A thin-walled metal spherical shell has a radius $$25.0 cm$$ and charge $$2.00 \times 10^{-7} C$$. Find E for a point (a) inside the shell, (b) just outside it, and (c) $$3.00 m$$ from the center.
A charged cloud system produces an electric field in the air near Earth's surface. A particle of charge $$-2.0\times 10^{-9}\ C$$ is acted on by a downward electrostatic force of $$3.0\times 10^{-6}\ N$$ when placed in this field. What is the magnitude of the electric field?
An infinitely long line charge having a uniform charge per unit length $$\lambda$$ lies at a distance $$d$$ from point $$O$$ as shown in Fig. Determine the total electric flux through the surface of a sphere of radius $$R$$ centred at $$O$$ resulting from this line charge. Consider both cases where $$R < d$$ and $$R > d$$.
The dielectric strength of air is $$3.0\times 10^{6} N/C$$. Find the largest charge (in $$nC$$) that a metallic sphere of $$3\ mm$$ radius can hold.
Two identical conducting small spheres are placed with their centres $$0.300m$$ apart. One is given a charge of $$12.0nC$$ and the other a charge of $$-10.0nC$$. (a) Find the electric force exerted by one sphere on the other (b) If the spheres are connected by a conducting wire, find the electric force between the two after they attain equilibrium.