359379
Two charges \({+q}\) and \({-q}\) are placed as shown in figure. The potential difference \({V_{A}-V_{B}}\) is
1 Zero
2 \({\dfrac{q d}{4 \pi \varepsilon_{0}(a+d)}}\)
3 \({-\dfrac{q d}{4 \pi \varepsilon_{0}(a+d)}}\)
4 \({\dfrac{q d}{2 \pi \varepsilon_{0} a(a+d)}}\)
Explanation:
The potentials at \({A}\) and \({B}\) are \({V_{A}=\dfrac{k q}{a}+\dfrac{k(-q)}{a+d}=\dfrac{k q d}{a(a+d)}}\) \({V_{B}=\dfrac{k q}{(a+d)}+\dfrac{k(-q)}{a}=-\dfrac{k q d}{a(a+d)}}\) There for \({V_{A}-V_{B}=\dfrac{2 k q d}{a(a+d)}=\dfrac{q d}{2 \pi \varepsilon_{0} a(a+d)}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359380
Two unlike charge of magnitude \(q\) are seperated by a distance \(5 d\). The potential at a point midway between them
Due to unlike charges potential at a point midway between them is zero. \(\begin{aligned}V_{n e t} & =\dfrac{K q}{4 \pi \varepsilon_{0} \dfrac{5 d}{2}}+\dfrac{(-K q)}{4 \pi \varepsilon_{0} \dfrac{5 d}{2}} \\V_{n e t} & =\text { Zero }\end{aligned}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359381
Four point charges \( - Q, - q,2q\) and \(2Q\) are placed, one at each corner of the square. The relation between \(Q\) and \(q\) for which the potential at the centre of the square is zero, is:
1 \(Q = - q\)
2 \(\frac{1}{q}\)
3 \(Q = q\)
4 \(Q = - \frac{1}{q}\)
Explanation:
If potential at centre is zero, then \({V_1} + {V_2} + {V_3} + {V_4} = 0\) \( - \frac{{kQ}}{r} - \frac{{kq}}{r} + \frac{{k2Q}}{r} + \frac{{k2q}}{r} = 0\) \( - Q - q + 2q + 2Q = 0\) \(Q = - q\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359382
Four electric charges \({+q,+q,-q}\) and \({-q}\) are placed at the corners of a square of side \({2 L}\) (see figure). The electric potential at point \({A}\), midway between the two charges \({+q}\) and \({+q}\) is
359379
Two charges \({+q}\) and \({-q}\) are placed as shown in figure. The potential difference \({V_{A}-V_{B}}\) is
1 Zero
2 \({\dfrac{q d}{4 \pi \varepsilon_{0}(a+d)}}\)
3 \({-\dfrac{q d}{4 \pi \varepsilon_{0}(a+d)}}\)
4 \({\dfrac{q d}{2 \pi \varepsilon_{0} a(a+d)}}\)
Explanation:
The potentials at \({A}\) and \({B}\) are \({V_{A}=\dfrac{k q}{a}+\dfrac{k(-q)}{a+d}=\dfrac{k q d}{a(a+d)}}\) \({V_{B}=\dfrac{k q}{(a+d)}+\dfrac{k(-q)}{a}=-\dfrac{k q d}{a(a+d)}}\) There for \({V_{A}-V_{B}=\dfrac{2 k q d}{a(a+d)}=\dfrac{q d}{2 \pi \varepsilon_{0} a(a+d)}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359380
Two unlike charge of magnitude \(q\) are seperated by a distance \(5 d\). The potential at a point midway between them
Due to unlike charges potential at a point midway between them is zero. \(\begin{aligned}V_{n e t} & =\dfrac{K q}{4 \pi \varepsilon_{0} \dfrac{5 d}{2}}+\dfrac{(-K q)}{4 \pi \varepsilon_{0} \dfrac{5 d}{2}} \\V_{n e t} & =\text { Zero }\end{aligned}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359381
Four point charges \( - Q, - q,2q\) and \(2Q\) are placed, one at each corner of the square. The relation between \(Q\) and \(q\) for which the potential at the centre of the square is zero, is:
1 \(Q = - q\)
2 \(\frac{1}{q}\)
3 \(Q = q\)
4 \(Q = - \frac{1}{q}\)
Explanation:
If potential at centre is zero, then \({V_1} + {V_2} + {V_3} + {V_4} = 0\) \( - \frac{{kQ}}{r} - \frac{{kq}}{r} + \frac{{k2Q}}{r} + \frac{{k2q}}{r} = 0\) \( - Q - q + 2q + 2Q = 0\) \(Q = - q\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359382
Four electric charges \({+q,+q,-q}\) and \({-q}\) are placed at the corners of a square of side \({2 L}\) (see figure). The electric potential at point \({A}\), midway between the two charges \({+q}\) and \({+q}\) is
359379
Two charges \({+q}\) and \({-q}\) are placed as shown in figure. The potential difference \({V_{A}-V_{B}}\) is
1 Zero
2 \({\dfrac{q d}{4 \pi \varepsilon_{0}(a+d)}}\)
3 \({-\dfrac{q d}{4 \pi \varepsilon_{0}(a+d)}}\)
4 \({\dfrac{q d}{2 \pi \varepsilon_{0} a(a+d)}}\)
Explanation:
The potentials at \({A}\) and \({B}\) are \({V_{A}=\dfrac{k q}{a}+\dfrac{k(-q)}{a+d}=\dfrac{k q d}{a(a+d)}}\) \({V_{B}=\dfrac{k q}{(a+d)}+\dfrac{k(-q)}{a}=-\dfrac{k q d}{a(a+d)}}\) There for \({V_{A}-V_{B}=\dfrac{2 k q d}{a(a+d)}=\dfrac{q d}{2 \pi \varepsilon_{0} a(a+d)}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359380
Two unlike charge of magnitude \(q\) are seperated by a distance \(5 d\). The potential at a point midway between them
Due to unlike charges potential at a point midway between them is zero. \(\begin{aligned}V_{n e t} & =\dfrac{K q}{4 \pi \varepsilon_{0} \dfrac{5 d}{2}}+\dfrac{(-K q)}{4 \pi \varepsilon_{0} \dfrac{5 d}{2}} \\V_{n e t} & =\text { Zero }\end{aligned}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359381
Four point charges \( - Q, - q,2q\) and \(2Q\) are placed, one at each corner of the square. The relation between \(Q\) and \(q\) for which the potential at the centre of the square is zero, is:
1 \(Q = - q\)
2 \(\frac{1}{q}\)
3 \(Q = q\)
4 \(Q = - \frac{1}{q}\)
Explanation:
If potential at centre is zero, then \({V_1} + {V_2} + {V_3} + {V_4} = 0\) \( - \frac{{kQ}}{r} - \frac{{kq}}{r} + \frac{{k2Q}}{r} + \frac{{k2q}}{r} = 0\) \( - Q - q + 2q + 2Q = 0\) \(Q = - q\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359382
Four electric charges \({+q,+q,-q}\) and \({-q}\) are placed at the corners of a square of side \({2 L}\) (see figure). The electric potential at point \({A}\), midway between the two charges \({+q}\) and \({+q}\) is
359379
Two charges \({+q}\) and \({-q}\) are placed as shown in figure. The potential difference \({V_{A}-V_{B}}\) is
1 Zero
2 \({\dfrac{q d}{4 \pi \varepsilon_{0}(a+d)}}\)
3 \({-\dfrac{q d}{4 \pi \varepsilon_{0}(a+d)}}\)
4 \({\dfrac{q d}{2 \pi \varepsilon_{0} a(a+d)}}\)
Explanation:
The potentials at \({A}\) and \({B}\) are \({V_{A}=\dfrac{k q}{a}+\dfrac{k(-q)}{a+d}=\dfrac{k q d}{a(a+d)}}\) \({V_{B}=\dfrac{k q}{(a+d)}+\dfrac{k(-q)}{a}=-\dfrac{k q d}{a(a+d)}}\) There for \({V_{A}-V_{B}=\dfrac{2 k q d}{a(a+d)}=\dfrac{q d}{2 \pi \varepsilon_{0} a(a+d)}}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359380
Two unlike charge of magnitude \(q\) are seperated by a distance \(5 d\). The potential at a point midway between them
Due to unlike charges potential at a point midway between them is zero. \(\begin{aligned}V_{n e t} & =\dfrac{K q}{4 \pi \varepsilon_{0} \dfrac{5 d}{2}}+\dfrac{(-K q)}{4 \pi \varepsilon_{0} \dfrac{5 d}{2}} \\V_{n e t} & =\text { Zero }\end{aligned}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359381
Four point charges \( - Q, - q,2q\) and \(2Q\) are placed, one at each corner of the square. The relation between \(Q\) and \(q\) for which the potential at the centre of the square is zero, is:
1 \(Q = - q\)
2 \(\frac{1}{q}\)
3 \(Q = q\)
4 \(Q = - \frac{1}{q}\)
Explanation:
If potential at centre is zero, then \({V_1} + {V_2} + {V_3} + {V_4} = 0\) \( - \frac{{kQ}}{r} - \frac{{kq}}{r} + \frac{{k2Q}}{r} + \frac{{k2q}}{r} = 0\) \( - Q - q + 2q + 2Q = 0\) \(Q = - q\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359382
Four electric charges \({+q,+q,-q}\) and \({-q}\) are placed at the corners of a square of side \({2 L}\) (see figure). The electric potential at point \({A}\), midway between the two charges \({+q}\) and \({+q}\) is
