What is the magnitude of the electric field at the dot in the figure?

A. What is the magnitude of the electric field at the dot in the figure?

B. What is the direction of the electric field at the dot in the figure? Choose best answer.

(a) the negative x-axis.

(b) the positive x-axis.

(c) 45 below -x-axis

(d) 45 below +x-axis


Answer

Part A. The expression for the strength of the electric field E in terms of the potential difference $V$ and the separation between the plates d is given by,

E=\frac{V}{d}

Substitute 200 \mathrm{~V} for \mathrm{V} and 1.0 \mathrm{~cm} for \mathrm{d} in above equation as follows:

E=\frac{200 \mathrm{~V}}{1.0 \mathrm{~cm}\left(\frac{10^{-2} \mathrm{~m}}{1 \mathrm{~cm}}\right)}

=20,000 \mathrm{~V} / \mathrm{m}

After rounding off the final answer to two significant figures the strength of the electric field is 2.0 \times 10^{4} \mathrm{~V} / \mathrm{m}.

Part A The strength of the electric field is 2.0 \times 10^{4} \mathrm{~V} / \mathrm{m}.


Part B From the figure it is clear that the equipotential lines are parallel to each other and one of them is passing through the dot. The following figure shows the direction of the electric field. The line drawn perpendicular to the equipotential lines and passing through the dot represents the direction of the electric field. So, a perpendicular line is drawn to the equipotential lines from the dot. Now, used the property of triangle that is total angle is equal to 180 degrees. From the rule of triangle, if two of the angles are 90 degrees and 45 degrees, then the third angle must be equal to 45 degrees only. Thus, from the above provided figure, it can be concluded that the angle made by the electric field with x-axis is 45 degrees and it is measured below the negative x-axis.

Part B The electric field makes an angle of 45^{\circ} with the negative x-axis.

Explanation

The equipotential lines making an angle of 45^{\circ} with the x-axis and the equipotential lines and electric field lines are perpendicular to each other and the equipotential lines, electric field and the x-axis forms right angled triangle. In the triangle the sum of the angles is 180^{\circ}. The sum of the two angles is 135^{\circ} and hence, the other angle should be 45^{\circ}. There, the concept of vertically opposite angles is used to find the angle made by the electric field.

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