P.3.7.3.3 Electric potential

Four positive charges are fixed at the corners of a square as shown.

The total potential at the centre of the square, a distance d from each charge, is (5Q) / (4πε₀d).

Three of the charges have a charge of +Q. What is the magnitude of the fourth charge?

• -7Q/4

• Q

• √2Q

• 2Q

An α particle makes a head−on collision with a gold nucleus containing 79 protons. The distance of closest approach of the α particle to the nucleus is 4.0 × 10⁻¹⁴ m.

What electrostatic force acts on the gold nucleus when at this separation?

• 9.1 × 10⁻¹¹ N

• 23 N

• 290 N

• 1.4 × 10²⁰ N

Two fixed parallel metal plates P and Q are at constant electrical potentials of +100 V and +70 V respectively. A proton travelling from P to Q experiences a force F due to the electric field between P and Q, and a change of potential energy of ΔE_p.

Which line, A to D, in the table gives the direction of F and the value of ΔE_p?

• A

• B

• C

• D

The diagram shows the field lines in a region of an electric field created by a positive charge.

Which one of the following statements is correct?

When moving from X to Y

• the electric potential is constant.

• the electric potential increases.

• the electric potential decreases.

• the electric potential changes from positive to negative.

The diagram shows two point charges of magnitude +Q and −2Q placed a distance r apart.

What is the electric potential at point P, a distance r to the right of the −2Q charge?

• 
• 
• 
• 

The potentials at points R and S due to the +5.0 nC charge are 375 V and 450 V respectively. How much work is done when a +2.0 nC charge is moved from R to S?

• 0.12 μJ

• 0.15 μJ

• 0.19 μJ

• 0.38 μJ

In the equation X = ab / rⁿ , X represents a physical variable in an electric or a gravitational field, a is a constant, b is either mass or charge and n is a number.

Which line, A to D, in the table provides a consistent representation of X, a and b according to the value of n?

The symbols E, g, V and r have their usual meanings.

• A

• B

• C

• D

Two identical positive point charges, P and Q, are separated by a distance of 4.0 m.

The resultant electric potential at point M, which is mid-way between the charges, is 25.0 V.

What would be the resultant electrical potential at a point 1.0 m closer to P?

• 8.3 V

• 12.5 V

• 33.3 V

• 37.5 V

The diagram below shows the field lines and equipotential lines around an isolated positive point charge.

Which one of the following statements concerning the work done when a small charge is moved in the field is incorrect?

• when it is moved from either P to Q or S to R, the work done is the same in each case

• when it is moved from Q to R no work is done

• when it is moved around the path PQRS, the overall work done is zero

• when it is moved around the path PQRS, the overall work done is equal to twice the work done in moving from P to Q

A uniform electric field of electric field strength E is aligned so it is vertical. An ion moves vertically through a small distance Δd from point X to point Y in the field.

There is a uniform gravitational field of field strength g throughout the region.

Which line, A to D, in the table correctly gives the gravitational potential difference, and the electric potential difference, between X and Y?

• A

• B

• C

• D