Electric potential at any point is V = - 5x + 3y + √ {15} z , then magnitude of electric field is

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2. Electric Potential and Capacitance

medium

Electric potential at any point is $V = - 5x + 3y + \sqrt {15} z$, then the magnitude of the electric field is

$3\sqrt 2 $

$4\sqrt 2 $

$5\sqrt 2 $

$7$

Solution

(d) ${E_x} = – \frac{{dV}}{{dx}} = – ( – 5) = 5;$${E_y} = – \frac{{dV}}{{dy}} = – 3$
and ${E_z} = – \frac{{dV}}{{dz}} = – \sqrt {15} $
${E_{net}} = \sqrt {E_x^2 + E_y^2 + E_z^2} = \sqrt {{{(5)}^2} + {{( – 3)}^2} + {{( – \sqrt {15} )}^2}} = 7$

Standard 12

Physics

If on the $x$-axis electric potential decreases uniformly from $60 \,V$ to $20 \,V$ between $x=-2 \,m$ to $x=+2 \,m$, then the magnitude of electric field at the origin

medium

Electric potential is given by

$V = 6x – 8x{y^2} – 8y + 6yz – 4{z^2}$

Then electric force acting on $2\,C$ point charge placed on origin will be……$N$

medium

The electric potential in a region is represented as $V = 2x + 3y -z$ ; then the expression of electric field strength is

medium

A charge of $5\,C$ experiences a force of $5000\,N$ when it is kept in a uniform electric field. ………$V$ is the potential difference between two points separated by a distance of $1\,cm$

easy

Determine the electric field strength vector if the potential of this field depends on $x, y$ coordinates as $V=10$ axy

medium

Electric potential at any point is $V = - 5x + 3y + \sqrt {15} z$, then the magnitude of the electric field is

Solution

Similar Questions

If on the $x$-axis electric potential decreases uniformly from $60 \,V$ to $20 \,V$ between $x=-2 \,m$ to $x=+2 \,m$, then the magnitude of electric field at the origin

Electric potential is given by $V = 6x – 8x{y^2} – 8y + 6yz – 4{z^2}$ Then electric force acting on $2\,C$ point charge placed on origin will be……$N$

The electric potential in a region is represented as $V = 2x + 3y -z$ ; then the expression of electric field strength is

A charge of $5\,C$ experiences a force of $5000\,N$ when it is kept in a uniform electric field. ………$V$ is the potential difference between two points separated by a distance of $1\,cm$

Determine the electric field strength vector if the potential of this field depends on $x, y$ coordinates as $V=10$ axy

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Electric potential is given by

$V = 6x – 8x{y^2} – 8y + 6yz – 4{z^2}$

Then electric force acting on $2\,C$ point charge placed on origin will be……$N$