A point charge $q$ is held at the centre of a circle of radius $r . B, C$ are two points on the circumference of the circle and $A$ is a point outside the circle. If $W_{A B}$ represents work done by electric field in taking a charge $q_0$ from $A$ to $B$ and $W_{A C}$ represents the workdone from $A$ to $C$, then
A point charge $q$ is held at the centre of a circle of radius $r . B, C$ are two points on the circumference of the circle and $A$ is a point outside the circle. If $W_{A B}$ represents work done by electric field in taking a charge $q_0$ from $A$ to $B$ and $W_{A C}$ represents the workdone from $A$ to $C$, then
- A
$W_{A B} > W_{A C}$
- B
$W_{A B} < W_{A C}$
- C
$W_{A B}=W_{A C} \neq 0$
- D
$W_{A B}=W_{A C}=0$
Similar Questions
A disk of radius $R$ with uniform positive charge density $\sigma$ is placed on the $x y$ plane with its center at the origin. The Coulomb potential along the $z$-axis is
$V(z)=\frac{\sigma}{2 \epsilon_0}\left(\sqrt{R^2+z^2}-z\right)$
A particle of positive charge $q$ is placed initially at rest at a point on the $z$ axis with $z=z_0$ and $z_0>0$. In addition to the Coulomb force, the particle experiences a vertical force $\vec{F}=-c \hat{k}$ with $c>0$. Let $\beta=\frac{2 c \epsilon_0}{q \sigma}$. Which of the following statement($s$) is(are) correct?
$(A)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{25}{7} R$, the particle reaches the origin.
$(B)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{3}{7} R$, the particle reaches the origin.
$(C)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{R}{\sqrt{3}}$, the particle returns back to $z=z_0$.
$(D)$ For $\beta>1$ and $z_0>0$, the particle always reaches the origin.
A disk of radius $R$ with uniform positive charge density $\sigma$ is placed on the $x y$ plane with its center at the origin. The Coulomb potential along the $z$-axis is
$V(z)=\frac{\sigma}{2 \epsilon_0}\left(\sqrt{R^2+z^2}-z\right)$
A particle of positive charge $q$ is placed initially at rest at a point on the $z$ axis with $z=z_0$ and $z_0>0$. In addition to the Coulomb force, the particle experiences a vertical force $\vec{F}=-c \hat{k}$ with $c>0$. Let $\beta=\frac{2 c \epsilon_0}{q \sigma}$. Which of the following statement($s$) is(are) correct?
$(A)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{25}{7} R$, the particle reaches the origin.
$(B)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{3}{7} R$, the particle reaches the origin.
$(C)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{R}{\sqrt{3}}$, the particle returns back to $z=z_0$.
$(D)$ For $\beta>1$ and $z_0>0$, the particle always reaches the origin.
- [IIT 2022]
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A test charge $q$ is made to move in the electric field of a point charge $Q$ along two different closed paths as per figure. First path has sections along and perpendicular to lines of electric field. Second path is a rectangular loop of the same area as the first loop. How does the work done compare in the two cases ?
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- [JEE MAIN 2019]
The work done to take an electron from rest where potential is $-60\, V$ to another point where potential is $-20\, V$ is given by.....$eV$
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