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Question
An electric field →E=(2^i+3^j)N/C exists in space. The potential difference (VP−VQ) between two points P and Q whose position vectors →rP=^i+2^j and →rQ=2^i+^j+^k is
An electric field →E=(2^i+3^j)N/C exists in space. The potential difference (VP−VQ) between two points P and Q whose position vectors →rP=^i+2^j and →rQ=2^i+^j+^k is
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Solution
The correct option is A −1 V
Position vector →rPQ=→rQ−→rP
∴ →rPQ=(2^i+^j+^k)−(^i+2^j)=^i−^j+^k
Potential difference VQ−VP=−→E.→rPQ
∴ VQ−VP=−(2^i+3^j).(^i−^j+^k)=−(2−3)=1 V
⟹ VP−VQ=−1 V
Position vector →rPQ=→rQ−→rP
∴ →rPQ=(2^i+^j+^k)−(^i+2^j)=^i−^j+^k
Potential difference VQ−VP=−→E.→rPQ
∴ VQ−VP=−(2^i+3^j).(^i−^j+^k)=−(2−3)=1 V
⟹ VP−VQ=−1 V
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