Q4MCQ Figure 16鈥�50 shows electric fi... [FREE SOLUTION]

Chapter 16: Q4MCQ (page 443)

Figure 16鈥�50 shows electric field lines due to a point charge. What can you say about the field at point 1 compared with the field at point 2?
(a) The field at point 2 is larger, because point 2 is on a field line.
(b) The field at point 1 is larger, because point 1 is not on a field line.
(c) The field at point 1 is zero, because point 1 is not on a field line.
(d) The field at point 1 is larger, because the field lines are closer together in that region.

Short Answer

Expert verified

The correct answer is option (d) The field at point 1 is larger because the field lines are closer together in that region.

Step by step solution

Understanding the electric field lines

The electric field lines indicate the direction of the electric field. The magnitude of the electric field depends on the density of field lines. More density of field lines indicates the stronger electric field.

Comparison of the electric field at different points

You can assume the field is zero as there is not any field line through point 1. But your assumption is wrong.

You can think that in the nearest point 1, the field line's density is more than the density of field lines at point 2.

In addition, you know the more the density of field lines, the more the electric field is. Therefore, the field at point 1 is larger as the field lines are closer together in that region.

The electric field due to a point charge is given as:

\(E = \frac{{kQ}}{r}\) 鈥� (i)

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

From equation (i), it is also clear that the magnitude of the electric field is inversely proportional to the distance from the charge. Since the distance of point 2 is more than that of point 1 therefore, the electric field at point 1 is larger.

Thus, the correct option is (d).