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Chapter 17: Q3MCQ (page 473)

Four identical point charges are arranged at the corners of a square [Hint: Draw a figure]. The electric field E and potential V at the centre of the square are

(a) \(E = 0\), \(V = 0\).

(b) \(E = 0\), \(V \ne 0\).

(c) \(E \ne 0\), \(V \ne 0\).

(d) \(E \ne 0\), \(V = 0\).

(e) \(E = V\) regardless of the value.

Short Answer

Expert verified

The correct answer is option (b) \(E = 0\), \(V \ne 0\).

Step by step solution

01

Understanding the electric field

The presence of an electric field is only due to the difference in electric potential between two points in space. The electric field is the gradient of electric potential. It inversely depends on the distance of a point from a charge.

02

Evaluation of the values of electric field and electric potential

The electric field at any point due to a point charge is given by,

\(\overrightarrow E = \frac{{kQ}}{{{r^2}}}\hat r\)

Here, k is the Coulomb鈥檚 constant, Q is the charge and r is the distance.

The electric field is a vector quantity. Since all the charges placed at the corners of a square are identical, the magnitude of electric field at the centre of the square due to all four charges is the same but in different directions. At the centre of the square, they add up to give a net electric field zero.

The electric potential is given as:

\(V = \frac{{kQ}}{r}\)

Electric potential is a scalar quantity. Therefore, the electric potential due to four identical charges has some value at the centre of the square.

Therefore, at the centre,\(E = 0;\;V \ne 0\)

Thus, the correct option is (b).

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Most popular questions from this chapter

(III) In the Bohr model of the hydrogen atom, an electron orbits a proton (the nucleus) in a circular orbit of radius \({\bf{0}}{\bf{.53 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\;{\bf{m}}\). (a) What is the electric potential at the electron鈥檚 orbit due to the proton? (b) What is the kinetic energy of the electron? (c) What is the total energy of the electron in its orbit? (d) What is the ionization energy鈥� that is, the energy required to remove the electron from the atom and take it to \({\bf{r = }}\infty \), at rest? Express the results of parts (b), (c), and (d) in joules and eV.

A dielectric is pulled out from between the plates of a capacitor which remains connected to a battery. What changes occur to (a) the capacitance, (b) the charge on the plates, (c) the potential difference, (d) the energy stored in the capacitor, and (e) the electric field? Explain your answers.

If a negative charge is initially at rest in an electric field, will it move toward a region of higher potential or lower potential? What about a positive charge? How does the potential energy of the charge change in each instance? Explain.

Question: Near the surface of the Earth there is an electric field of about \({\bf{150}}\;{{\bf{V}} \mathord{\left/{\vphantom {{\bf{V}} {\bf{m}}}} \right.} {\bf{m}}}\)which points downward. Two identical balls with mass \({\bf{m = 0}}{\bf{.670}}\;{\bf{kg}}\) are dropped from a height of 2.00 m, but one of the balls is positively charged with \({{\bf{q}}_{\bf{1}}}{\bf{ = 650}}\;{\bf{\mu C}}\), and the second is negatively charged with \({{\bf{q}}_{\bf{2}}}{\bf{ = }} - {\bf{650}}\;{\bf{\mu C}}\). Use conservation of energy to determine the difference in the speed of the two balls when they hit the ground. (Neglect air resistance.)

(I) What is the electric potential 15.0 cm from a \({\bf{3}}{\bf{.00}}\;{\bf{\mu C}}\) point charge?
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