Electric Charges And Fields

Q: Two identical charged spheres suspended from a common distance \$d(d < < 1)\$ apart because of their mutual repulsion. The charged begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity \$v\$. Then \$v\$ varies as a function of the distance \$x\$ between the spheres, as

From figure \$\tan \theta = \dfrac {F_{e}}{mg} =\theta\$\$\dfrac {kq^{2}}{x^{2}mg} = \dfrac {x}{2l}\$or \$x^{3}\propto q^{2} .... (1)\$or \$x^{3/2} \propto q ..... (2)\$Differentiating eq. \$(1)\$ w.r.t time\$3x^{2} \dfrac {dx}{dt}\propto 2q \dfrac {dq}{dt}\$ but \$\dfrac {dq}{dt}\$ is constantso \$x^{2}(v) \propto q\$ Replace \$q\$ from eq. \$(2)\$\$x^{2}(v) \propto x^{3/2}\$ or \$v\propto x^{-1/2}\$.

Q: An electric line of force in the \$xy-plane\$ is given by equation \$x^{2} + y^{2} = 1\$. A particle with unit positive charge, initially at rest at the point \$x = 1, y = 0\$ in the \$xy - plane\$.

Charge will move along the circular line of force because \$x^{2} + y^{2} = 1\$ is the equation of circle in \$xy - plane\$.

Question

Two identical charged spheres suspended from a common distance $d (d < < 1)$ apart because of their mutual repulsion. The charged begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity $v$ . Then $v$ varies as a function of the distance $x$ between the spheres, as

Electric Charges And Fields

Physics
6594 Views

An electric line of force in the $x y - p l a n e$ is given by equation $x^{2} + y^{2} = 1$ . A particle with unit positive charge, initially at rest at the point $x = 1, y = 0$ in the $x y - p l a n e$ .

Electric Charges And Fields

Physics 6594 Views

An electric line of force in the xy−plane is given by equation x2+y2=1. A particle with unit positive charge, initially at rest at the point x=1,y=0 in the xy−plane.

Physics
6594 Views

An electric line of force in the $x y - p l a n e$ is given by equation $x^{2} + y^{2} = 1$ . A particle with unit positive charge, initially at rest at the point $x = 1, y = 0$ in the $x y - p l a n e$ .