A conducting sphere of radius $$R$$ is given a charge $$Q.$$ The electric potential and the electric field at the centre of the sphere respectively are
A.
zero and $$\frac{Q}{{4\pi {\varepsilon _0}{R^2}}}$$
B.
$$\frac{Q}{{4\pi {\varepsilon _0}R}}$$ and zero
C.
$$\frac{Q}{{4\pi {\varepsilon _0}R}}{\text{and}}\frac{Q}{{4\pi {\varepsilon _0}{R^2}}}$$
D.
Both and zero
Answer :
$$\frac{Q}{{4\pi {\varepsilon _0}R}}$$ and zero
Solution :
In a conducting sphere charge is present on the surface of the sphere. So, electric field inside will be zero and potential remains constant from centre to surface of sphere and is equal to $$\frac{1}{{4\pi {\varepsilon _0}}}\frac{Q}{R}$$
Releted MCQ Question on Electrostatics and Magnetism >> Electric Potential
Releted Question 1
If potential (in volts) in a region is expressed as $$V\left( {x,y,z} \right) = 6xy - y + 2yz,$$ electric field (in $$N/C$$ ) at point $$\left( {1,1,0} \right)$$ is
A.
$$ - \left( {3\hat i + 5\hat j + 3\hat k} \right)$$
B.
$$ - \left( {6\hat i + 5\hat j + 2\hat k} \right)$$
C.
$$ - \left( {2\hat i + 3\hat j + \hat k} \right)$$
D.
$$ - \left( {6\hat i + 9\hat j + \hat k} \right)$$
A conducting sphere of radius $$R$$ is given a charge $$Q.$$ The electric potential and the electric field at the centre of the sphere respectively are
A.
zero and $$\frac{Q}{{4\pi {\varepsilon _0}{R^2}}}$$
B.
$$\frac{Q}{{4\pi {\varepsilon _0}R}}$$ and zero
C.
$$\frac{Q}{{4\pi {\varepsilon _0}R}}{\text{and}}\frac{Q}{{4\pi {\varepsilon _0}{R^2}}}$$
In a region, the potential is represented by $$V\left( {x,y,z} \right) = 6x - 8xy - 8y + 6yz,$$ where $$V$$ is in volts and $$x,y,z$$ are in metres. The electric force experienced by a charge of $$2C$$ situated at point $$\left( {1,1,1} \right)$$ is
Four point charges $$ - Q, - q,2q$$ and $$2Q$$ are placed, one at each corner of the square. The relation between $$Q$$ and $$q$$ for which the potential at the centre of the square is zero, is