Question

A −10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis. What is the electric potential at the point on the x-axis where the electric field is zero?

Accepted Answer

Step 1: Understand the problem. The electric field is zero at a point where the contributions from both charges cancel each other out. This point is not necessarily the midpoint between the charges because the magnitudes of the charges are different. Use the principle of superposition to find this point. Step 2: Set up the equation for the electric field. The electric field due to a point charge is given by $$ E = \frac{k \cdot q}{r^2} $$, where $$ k  is $$Coulomb's constant, $$ q  is $$the charge, and $$ r  is $$the distance from the charge. At the point where the electric field is zero, the magnitudes of the electric fields from both charges are equal: $$ \frac{k \cdot q_1}{r_1^2} = \frac{k \cdot q_2}{r_2^2} . $$Step 3: Solve for the distance $$ r_1 $$ and $$ r_2 . $$Let $$ r_1  be $$the distance from the −10.0 nC charge to the point where the electric field is zero, and $$ r_2  be $$the distance from the +20.0 nC charge to the same point. Since the charges are 15.0 cm apart, $$ r_1 + r_2 = 15.0 \, 	ext{cm} . $$Substitute $$ r_2 = 15.0 \, 	ext{cm} - r_1 $$ into the equation from Step 2. Step 4: Calculate the electric potential at the point where the electric field is zero. The electric potential due to a point charge is given by $$ V = \frac{k \cdot q}{r} . At $$the point where the electric field is zero, the potentials from both charges add algebraically: $$ V = \frac{k \cdot q_1}{r_1} + \frac{k \cdot q_2}{r_2} . $$Use the values of $$ r_1 $$ and $$ r_2 $$ found in Step 3 to calculate the potential. Step 5: Verify the solution conceptually. Ensure that the electric field is indeed zero at the calculated point and that the electric potential is consistent with the principle of superposition. This step helps confirm the correctness of the approach and the calculations.

A −10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis. What is the electric potential at the point on the x-axis where the electric field is zero?

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Electric Charge

Electric Field

Electric Potential