(B) In a uniform electric field,the potential $V$ can be expressed as $V(x, y, z) = V_0 - (E_x x + E_y y + E_z z)$.Given $V(0, 0, 0) = 10 \ V$,so $V_0

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(B) In a uniform electric field,the potential $V$ can be expressed as $V(x, y, z) = V_0 - (E_x x + E_y y + E_z z)$.Given $V(0, 0, 0) = 10 \ V$,so $V_0 = 10 \ V$.Given $V(1, 0, 0) = 8 \ V$,so $10 - E_x(1) = 8 \implies E_x = 2 \ V$.Given $V(0, 1, 0) = 8 \ V$,so $10 - E_y(1) = 8 \implies E_y = 2 \ V$.Given $V(0, 0, 1) = 8 \ V$,so $10 - E_z(1) = 8 \implies E_z = 2 \ V$.Now,the potential at point $(1, 1, 1)$ is $V(1, 1, 1) = 10 - (2 \times 1 + 2 \times 1 + 2 \times 1) = 10 - 6 = 4 \ V$.

Class 12 Physics Electric Potential and Capacitance Electric potential

Medium

In a uniform electric field,the potential is $10 \ V$ at the origin of coordinates,and $8 \ V$ at each of the points $(1, 0, 0), (0, 1, 0)$ and $(0, 0, 1)$. The potential at the point $(1, 1, 1)$ will be....$V$

A
$0$
B
$4$
C
$8$
D
$10$

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Electric Potential and Capacitance

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Electric potential

The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$,having the same linear charge density $\lambda$,is $(\varepsilon_0 = \text{permittivity of free space})$

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$A$ charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R$ $(R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is

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Two concentric hollow metallic spheres of radii $r_1$ and $r_2$ $(r_1 > r_2)$ contain charges $q_1$ and $q_2$ respectively. The potential at a distance $x$ between $r_1$ and $r_2$ will be

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Four point charges $-Q, -q, 2q$ and $2Q$ are placed,one at each corner of a square. The relation between $Q$ and $q$ for which the potential at the center of the square is zero is:

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Two particles $A$ and $B$ having the same mass have charges $+q$ and $+4q$ respectively. When they are allowed to fall from rest through the same electric potential difference,the ratio of their speeds $v_A$ to $v_B$ will be:

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In a uniform electric field,the potential is $10 \ V$ at the origin of coordinates,and $8 \ V$ at each of the points $(1, 0, 0), (0, 1, 0)$ and $(0, 0, 1)$. The potential at the point $(1, 1, 1)$ will be....$V$

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The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$,having the same linear charge density $\lambda$,is $(\varepsilon_0 = \text{permittivity of free space})$

$A$ charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R$ $(R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is

Two concentric hollow metallic spheres of radii $r_1$ and $r_2$ $(r_1 > r_2)$ contain charges $q_1$ and $q_2$ respectively. The potential at a distance $x$ between $r_1$ and $r_2$ will be

Four point charges $-Q, -q, 2q$ and $2Q$ are placed,one at each corner of a square. The relation between $Q$ and $q$ for which the potential at the center of the square is zero is:

Two particles $A$ and $B$ having the same mass have charges $+q$ and $+4q$ respectively. When they are allowed to fall from rest through the same electric potential difference,the ratio of their speeds $v_A$ to $v_B$ will be:

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